Prof. Dr. Carsten Carstensen

Profil

• Adaptive Raumdiskretisierungen in vier Beispielen

  Quelle ↗

  Zeitraum: 01/2004 - 05/2006 Projektleitung: Prof. Dr. Carsten Carstensen

• Athina Konstantinidou - CISM-Teilnahme

  Quelle ↗

  Förderer: DFG Sachbeihilfe Zeitraum: 09/2005 - 09/2005 Projektleitung: Prof. Dr. Carsten Carstensen

• Central European Network for Teaching and Research in Academic Liaison (CENTRAL) 08 Analysis und Numerik partieller Differentialgleichungen

  Quelle ↗

  Förderer: DAAD Zeitraum: 03/2015 - 12/2018 Projektleitung: Prof. Dr. Carsten Carstensen, Prof. Dr. Alexander Mielke

• Computational Methods in Applied Mathematics CMAM-5

  Quelle ↗

  Zeitraum: 08/2012 - 09/2012 Projektleitung: Prof. Dr. Carsten Carstensen

• Computation in the Sciences, Workshop zur Vorbereitung eines internationalen GRK (Veranstaltung: 15.11-19.11.2010 Seoul)

  Quelle ↗

  Förderer: DFG sonstige Programme Zeitraum: 11/2010 - 11/2010 Projektleitung: Prof. Dr. Carsten Carstensen

• DFG FG 797/1: "Analysis and computation of microstructure in finite plasticity" - Teilprojekt P1-1: "Numerical algorithms for the simulation of finite plasticity with microstructures"

  Quelle ↗
  409-01-A · Algorithmik und Komplexität

  Förderer: DFG Forschungsgruppe Zeitraum: 06/2007 - 12/2012 Projektleitung: Prof. Dr. Carsten Carstensen

• DFG FG 797/2: "Analysis and computation of microstructure in finite plasticity" - Teilprojekt P1-1: "Numerical algorithms for the simulation of finite plasticity with microstructures"

  Quelle ↗
  409-01-A · Algorithmik und Komplexität

  Förderer: DFG Forschungsgruppe Zeitraum: 10/2010 - 06/2016 Projektleitung: Prof. Dr. Carsten Carstensen

• DFG-Forschungszentrum "Mathematik für Schlüsseltechnologien - MATHEON": Adaptive solution of parametric eigenvalue problems for partial differential equations (Teilprojekt C 22)

  Quelle ↗

  Förderer: DFG sonstige Programme Zeitraum: 04/2008 - 12/2008 Projektleitung: Prof. Dr. Carsten Carstensen

• DFG-Forschungszentrum "Mathematik für Schlüsseltechnologien - MATHEON": Adaptive solution of parametric eigenvalue problems for partial differential equations (Teilprojekt C 22) II

  Quelle ↗

  Förderer: DFG sonstige Programme Zeitraum: 06/2010 - 05/2014 Projektleitung: Prof. Dr. Carsten Carstensen

• DFG-Forschungszentrum "Mathematik für Schlüsseltechnologien - MATHEON": Computational Finance - Adaptive FE Algorithm for Option Evaluation (Teilprojekt E 6)

  Quelle ↗

  Förderer: DFG sonstige Programme Zeitraum: 01/2004 - 05/2006 Projektleitung: Prof. Dr. Carsten Carstensen

• DFG-Forschungszentrum "Mathematik für Schlüsseltechnologien - MATHEON": Numerical solution of differential equations (Teilprojekt C 13)

  Quelle ↗

  Förderer: DFG sonstige Programme Zeitraum: 06/2002 - 05/2010 Projektleitung: Prof. Dr. Carsten Carstensen

• DFG SPP 1480: Modellierung, Simulation und Kompensation von thermischen Bearbeitungseinflüssen für komplexe Zerspanprozesse

  Quelle ↗

  Förderer: DFG Sachbeihilfe Zeitraum: 09/2010 - 04/2014 Projektleitung: Prof. Dr. Carsten Carstensen

• Gemeinsame Forschungsvorhaben mit der Yonsei University in Seoul

  Quelle ↗

  Förderer: DAAD Zeitraum: 01/2011 - 12/2013 Projektleitung: Prof. Dr. Carsten Carstensen

• GRK 1128: Analysis, Numerics, and Optimisation of Multiphase Problems II

  Quelle ↗

  Förderer: DFG Graduiertenkolleg Zeitraum: 10/2009 - 09/2010 Projektleitung: Prof. Dr. Carsten Carstensen

• Joint Sino-German Project: The adaptive finite element method for the fourth order problem

  Quelle ↗

  Zeitraum: 10/2010 - 02/2013 Projektleitung: Prof. Dr. Carsten Carstensen

• Mathematische Modellierung und eff. Numerik zur Simulation von Werkzeugschleifen

  Quelle ↗
  411 · Konstruktion Maschinenbau und Produktionstechnik

  Förderer: DFG Sachbeihilfe Zeitraum: 04/2009 - 03/2011 Projektleitung: Prof. Dr. Carsten Carstensen

• Mathematische Modellierung und eff. Numerik zur Simulation von Werkzeugschleifen

  Quelle ↗
  411 · Konstruktion Maschinenbau und Produktionstechnik

  Förderer: DFG Sachbeihilfe Zeitraum: 06/2007 - 11/2010 Projektleitung: Prof. Dr. Carsten Carstensen

• Matheon VA:RMMM (Veranstaltung: 24.06.-26.06.2009, Berlin)

  Quelle ↗

  Zeitraum: 05/2009 - 09/2009 Projektleitung: Prof. Dr. Carsten Carstensen

• Numerische Relaxierung von nichtkonvexen Funktionalen der Festkörpermechanik

  Quelle ↗

  Förderer: DFG Sachbeihilfe Zeitraum: 09/2004 - 01/2007 Projektleitung: Prof. Dr. Carsten Carstensen

• Personenaustausch Indien

  Quelle ↗

  Förderer: DAAD Zeitraum: 09/2005 - 12/2007 Projektleitung: Prof. Dr. Carsten Carstensen

• Prognose und Beeinflussung der Wechselwirkungen von Strukturen und Prozessen

  Quelle ↗

  Förderer: DFG Sachbeihilfe Zeitraum: 08/2005 - 07/2007 Projektleitung: Prof. Dr. Carsten Carstensen

• Simulation und Anwendungen von Mikrostrukturen (Veranstaltung: 14.08.-18.08.06, Insel Föhr)

  Quelle ↗

  Förderer: Volkswagen Stiftung Zeitraum: 07/2006 - 12/2006 Projektleitung: Prof. Dr. Carsten Carstensen

• SPP 1748/1: Grundlagen und Anwendungen verallgemeinerter gemischter FEM für nichtlineare Probleme in der Festkörpermechanik

  Quelle ↗

  Förderer: DFG Sachbeihilfe Zeitraum: 09/2014 - 11/2019 Projektleitung: Prof. Dr. Carsten Carstensen, Prof. Dr.-Ing. habil. Dr. h.c. mult. Dr.-Ing. E. h. Peter Wriggers

• SPP 1748/2: Grundlagen und Anwendungen verallgemeinerter gemischter FEM für nichtlineare Probleme in der Festkörpermechanik

  Quelle ↗

  Förderer: DFG Schwerpunktprogramm Zeitraum: 10/2018 - 03/2023 Projektleitung: Prof. Dr. Carsten Carstensen

• Workshop Reliable Methods and Mathematical Modeling

  Quelle ↗

  Zeitraum: 07/2017 - 08/2017 Projektleitung: Prof. Dr. Carsten Carstensen

• Gesellschaft für angewandte Mathematik und Mechanik

  KPT

  147 Treffer85.0%
  • Workshop Reliable Methods and Mathematical Modeling
    K

    85.0%

• InnovationLab GmbH

  P

  87 Treffer62.6%
  • Interfaces in opto-electronic thin film multilayer devices
    P

    62.6%

• Peugeot Citroen Automobiles S.A.

  PT

  133 Treffer58.0%
  • EU: Monomer Sequence Control in Polymers: Toward Next-Generation Precision Materials (EURO-SEQUENCES)
    P

    58.0%

• Ionera Technologies GmbH

  PT

  134 Treffer58.0%
  • EU: Monomer Sequence Control in Polymers: Toward Next-Generation Precision Materials (EURO-SEQUENCES)
    P

    58.0%

• Science & Startups Berlin

  PT

  23 Treffer58.0%
  • Zuwendung im Rahmen des Programms „exist – Existenzgründungen aus der Wissenschaft“ aus dem Bundeshaushalt, Einzelplan 09, Kapitel 02, Titel 68607, Haushaltsjahr 2026, sowie aus Mitteln des Europäischen Strukturfonds (hier Euro-päischer Sozialfonds Plus – ESF Plus) Förderperiode 2021-2027 – Kofinanzierung für das Vorhaben: „exist Women“
    T

    58.0%

• International Business Machines Corporation Research GmbH

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  194 Treffer58.0%
  • EU: Simulation in Multiscale Physical and Biological Systems (STIMULATE)
    P

    58.0%
  • EU: Bottom-Up Generation of atomicalLy Precise syntheTIc 2D MATerials for High Performance in Energy and Electronic Applications – A Multi-Site Innovative Training Action (ULTIMATE)
    P

    56.2%

• NVIDIA GmbH

  PT

  61 Treffer58.0%
  • EU: Simulation in Multiscale Physical and Biological Systems (STIMULATE)
    P

    58.0%

• Magwel NV

  PT

  60 Treffer58.0%
  • EU: Simulation in Multiscale Physical and Biological Systems (STIMULATE)
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    58.0%

• ACCO SAS

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  88 Treffer57.9%
  • Lösung gekoppelter Probleme in der Nanoelektronik (nanoCOPS)
    P

    57.9%

• NXP Semiconductors Netherlands BV

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  87 Treffer57.9%
  • Lösung gekoppelter Probleme in der Nanoelektronik (nanoCOPS)
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    57.9%

• Non–convex potentials and microstructures in finite–strain plasticity

  2001

  Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 355 Zitationen · DOI

  A mathematical model for a finite–strain elastoplastic evolution problem is proposed in which one time–step of an implicit time–discretization leads to generally non–convex minimization problems. The elimination of all internal variables enables a mathematical and numerical analysis of a reduced problem within the general framework of calculus of variations and nonlinear partial differential equations. The results for a single slip–system and von Mises plasticity illustrate that finite–strain elastoplasticity generates reduced problems with non–quasiconvex energy densities and so allows for non–attainment of energy minimizers and microstructures.

• A posteriori error estimate for the mixed finite element method

  1997

  Mathematics of Computation · 276 Zitationen · DOI

  A computable error bound for mixed finite element methods is established in the model case of the Poisson–problem to control the error in the H(div, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Omega"> <mml:semantics> <mml:mi mathvariant="normal"> Ω </mml:mi> <mml:annotation encoding="application/x-tex">\Omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula> ) <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="times upper L squared left-parenthesis normal upper Omega right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo> × </mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal"> Ω </mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\times L^2(\Omega )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> –norm. The reliable and efficient a posteriori error estimate applies, e.g., to Raviart–Thomas, Brezzi-Douglas-Marini, and Brezzi-Douglas-Fortin-Marini elements.

• Axioms of adaptivity

  2014

  Computers & Mathematics with Applications · 234 Zitationen · DOI

  This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower bounds, inexact solvers, inhomogeneous boundary data, or the use of equivalent error estimators. Solely four axioms guarantee the optimality in terms of the error estimators. Compared to the state of the art in the temporary literature, the improvements of this article can be summarized as follows: First, a general framework is presented which covers the existing literature on optimality of adaptive schemes. The abstract analysis covers linear as well as nonlinear problems and is independent of the underlying finite element or boundary element method. Second, efficiency of the error estimator is neither needed to prove convergence nor quasi-optimal convergence behavior of the error estimator. In this paper, efficiency exclusively characterizes the approximation classes involved in terms of the best-approximation error and data resolution and so the upper bound on the optimal marking parameters does not depend on the efficiency constant. Third, some general quasi-Galerkin orthogonality is not only sufficient, but also necessary for the [Formula: see text]-linear convergence of the error estimator, which is a fundamental ingredient in the current quasi-optimality analysis due to Stevenson 2007. Finally, the general analysis allows for equivalent error estimators and inexact solvers as well as different non-homogeneous and mixed boundary conditions.

• Remarks around 50 lines of Matlab: short finite element implementation

  1999

  Numerical Algorithms · 210 Zitationen · DOI

• Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM

  2002

  Mathematics of Computation · 176 Zitationen · DOI

  Averaging techniques are popular tools in adaptive finite element methods for the numerical treatment of second order partial differential equations since they provide efficient a posteriori error estimates by a simple postprocessing. In this paper, their reliablility is shown for conforming, nonconforming, and mixed low order finite element methods in a model situation: the Laplace equation with mixed boundary conditions. Emphasis is on possibly unstructured grids, nonsmoothness of exact solutions, and a wide class of averaging techniques. Theoretical and numerical evidence supports that the reliability is up to the smoothness of given right-hand sides.

• Edge Residuals Dominate A Posteriori Error Estimates for Low Order Finite Element Methods

  1999

  SIAM Journal on Numerical Analysis · 171 Zitationen · DOI

  We prove that, up to higher order perturbation terms, edge residuals yield global upper and local lower bounds on the error of linear finite element methods both in H1 - and L2 -norms. We present two proofs: one uses the standard L2 -projection and the other relies on a new, weighted Clément-type interpolation operator.

• Breaking spaces and forms for the DPG method and applications including Maxwell equations

  2016

  Computers & Mathematics with Applications · 148 Zitationen · DOI

• Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods

  1999

  ESAIM Mathematical Modelling and Numerical Analysis · 144 Zitationen · DOI

  One of the main tools in the proof of residual-based a posteriori error estimates is a quasi-interpolation operator due to Clément. We modify this operator in the setting of a partition of unity with the effect that the approximation error has a local average zero. This results in a new residual-based a posteriori error estimate with a volume contribution which is smaller than in the standard estimate. For an elliptic model problem, we discuss applications to conforming, nonconforming and mixed finite element methods.

• Three Matlab Implementations of the Lowest-order Raviart-Thomas Mfem with a Posteriori Error Control

  2005

  Computational Methods in Applied Mathematics · 128 Zitationen · DOI

  Abstract The numerical approximation of the Laplace equation with inhomogeneous mixed boundary conditions in 2D with lowest-order Raviart-Thomas mixed finite elements is realized in three flexible and short MATLAB programs. It is the aim of this paper to derive, document, illustrate, and validate the three MATLAB implementations EBmfem, LMmfem, and CRmfem for further use and modification in education and research. A posteriori error control with a reliable and efficient averaging technique is included to monitor the discretization error. Therein, emphasis is on the correct treatment of mixed boundary conditions. Numerical examples illustrate some applications of the provided software and the quality of the error estimation.

• (ohne Titel)

  2002

  Computing · 126 Zitationen · DOI

• Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM

  2002

  Mathematics of Computation · 117 Zitationen · DOI

  Averaging techniques are popular tools in adaptive finite element methods since they provide efficient a posteriori error estimates by a simple postprocessing. In the second paper of our analysis of their reliability, we consider conforming <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="h"> <mml:semantics> <mml:mi>h</mml:mi> <mml:annotation encoding="application/x-tex">h</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -FEM of higher (i.e., not of lowest) order in two or three space dimensions. In this paper, reliablility is shown for conforming higher order finite element methods in a model situation, the Laplace equation with mixed boundary conditions. Emphasis is on possibly unstructured grids, nonsmoothness of exact solutions, and a wide class of local averaging techniques. Theoretical and numerical evidence supports that the reliability is up to the smoothness of given right-hand sides.

• A unifying theory of a posteriori error control for nonconforming finite element methods

  2007

  Numerische Mathematik · 116 Zitationen · DOI

• A posteriori error estimates for mixed FEM in elasticity

  1998

  Numerische Mathematik · 106 Zitationen · DOI

• Guaranteed lower bounds for eigenvalues

  2014

  Mathematics of Computation · 105 Zitationen · DOI

  This paper introduces fully computable two-sided bounds on the eigenvalues of the Laplace operator on arbitrarily coarse meshes based on some approximation of the corresponding eigenfunction in the nonconforming Crouzeix-Raviart finite element space plus some postprocessing. The efficiency of the guaranteed error bounds involves the global mesh-size and is proven for the large class of graded meshes. Numerical examples demonstrate the reliability of the guaranteed error control even with an inexact solve of the algebraic eigenvalue problem. This motivates an adaptive algorithm which monitors the discretisation error, the maximal mesh-size, and the algebraic eigenvalue error. The accuracy of the guaranteed eigenvalue bounds is surprisingly high with efficiency indices as small as 1.4.

• Fully Reliable Localized Error Control in the FEM

  1999

  SIAM Journal on Scientific Computing · 104 Zitationen · DOI

  If the first task in numerical analysis is the calculation of an approximate solution, the second is to provide a guaranteed error bound and is often of equal importance. The standard approaches in the a posteriori error analysis of finite element methods suppose that the exact solution has a certain regularity or thenumerical scheme enjoys some saturation property. For coarse meshes those asymptotic arguments are difficult to recast into rigorous error bounds. The aim of this paper is to provide reliable computable error bounds which are efficient and complete in the sense that constants are estimated as well. The main argument is a localization via a partition of unity which leads to problems on small domains. Two fully reliable estimates are established: The sharper one solves an analytical interface problem with residuals following Babuska and Rheinboldt [SIAM J. Numer. Anal., 15 (1978), pp. 736--754]. The second estimate is a modification of the standard residual-based a posteriori estimate with explicit constants from local analytical eigenvalue problems. For some class of triangulations we show that the efficiency constant is smaller than 2.5. According to our numerical experience, the overestimation of our computable estimates proved to be reasonably small, with an overestimation by a factor between 2.5 and 4 only.

• Modelling and simulation of process: machine interaction in grinding

  2008

  Production Engineering · 98 Zitationen · DOI

• Numerical solution of the scalar double-well problem allowing microstructure

  1997

  Mathematics of Computation · 95 Zitationen · DOI

  The direct numerical solution of a non-convex variational problem ( <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P"> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding="application/x-tex">P</mml:annotation> </mml:semantics> </mml:math> </inline-formula> ) typically faces the difficulty of the finite element approximation of rapid oscillations. Although the oscillatory discrete minimisers are properly related to corresponding Young measures and describe real physical phenomena, they are costly and difficult to compute. In this work, we treat the scalar double-well problem by numerical solution of the relaxed problem ( <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R upper P"> <mml:semantics> <mml:mrow> <mml:mi>R</mml:mi> <mml:mi>P</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">RP</mml:annotation> </mml:semantics> </mml:math> </inline-formula> ) leading to a (degenerate) convex minimisation problem. The problem ( <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R upper P"> <mml:semantics> <mml:mrow> <mml:mi>R</mml:mi> <mml:mi>P</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">RP</mml:annotation> </mml:semantics> </mml:math> </inline-formula> ) has a minimiser <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u"> <mml:semantics> <mml:mi>u</mml:mi> <mml:annotation encoding="application/x-tex">u</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and a related stress field <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma equals upper D upper W Superscript asterisk asterisk Baseline left-parenthesis nabla u right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi> σ </mml:mi> <mml:mo>=</mml:mo> <mml:mi>D</mml:mi> <mml:msup> <mml:mi>W</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo> ∗ </mml:mo> <mml:mo> ∗ </mml:mo> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal"> ∇ </mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>u</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\sigma = DW^{**}(\nabla {u})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which is known to coincide with the stress field obtained by solving ( <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P"> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding="application/x-tex">P</mml:annotation> </mml:semantics> </mml:math> </inline-formula> ) in a generalised sense involving Young measures. If <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u Subscript h"> <mml:semantics> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>h</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">u_h</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a finite element solution, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma Subscript h Baseline colon equals upper D upper W Superscript asterisk asterisk Baseline left-parenthesis nabla u Subscript h Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi> σ </mml:mi> <mml:mi>h</mml:mi> </mml:msub> <mml:mo>:=</mml:mo> <mml:mi>D</mml:mi> <mml:msup> <mml:mi>W</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo> ∗ </mml:mo> <mml:mo> ∗ </mml:mo> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal"> ∇ </mml:mi> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>u</mml:mi> </mml:mrow> <mml:mi>h</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\sigma _h:= D W^{**}(\nabla {u}_h)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the related discrete stress field. We prove a priori and a posteriori estimates for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma minus sigma Subscript h"> <mml:semantics> <mml:mrow> <mml:mi> σ </mml:mi> <mml:mo> − </mml:mo> <mml:msub> <mml:mi> σ </mml:mi> <mml:mi>h</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">\sigma -\sigma _h</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript 4 slash 3 Baseline left-parenthesis normal upper Omega right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>4</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:mo st

• Guaranteed lower eigenvalue bounds for the biharmonic equation

  2013

  Numerische Mathematik · 94 Zitationen · DOI

• Error reduction and convergence for an adaptive mixed finite element method

  2006

  Mathematics of Computation · 92 Zitationen · DOI

  An adaptive mixed finite element method (AMFEM) is designed to guarantee an error reduction, also known as saturation property: after each refinement step, the error for the fine mesh is strictly smaller than the error for the coarse mesh up to oscillation terms. This error reduction property is established here for the Raviart–Thomas finite element method with a reduction factor <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="rho greater-than 1"> <mml:semantics> <mml:mrow> <mml:mi> ρ </mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\rho &gt;1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> uniformly for the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L squared"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">L^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> norm of the flux errors. Our result allows for linear convergence of a proper adaptive mixed finite element algorithm with respect to the number of refinement levels. The adaptive algorithm surprisingly does not require any particular mesh design, unlike the conforming finite element method. The new arguments are a discrete local efficiency and a quasi-orthogonality estimate. The proof does not rely on duality or on regularity.

• An a posteriori error estimate for a first-kind integral equation

  1997

  Mathematics of Computation · 92 Zitationen · DOI

  In this paper we present a new a posteriori error estimate for the boundary element method applied to an integral equation of the first kind. The estimate is local and sharp for quasi-uniform meshes and so improves earlier work of ours. The mesh-dependence of the constants is analyzed and shown to be weaker than expected from our previous work. Besides the Galerkin boundary element method, the collocation method and the qualocation method are considered. A numerical example is given involving an adaptive feedback algorithm.

• Effective relaxation for microstructure simulations: algorithms and applications

  2004

  Computer Methods in Applied Mechanics and Engineering · 91 Zitationen · DOI

• Averaging techniques yield reliable a posteriori finite element error control for obstacle problems

  2004

  Numerische Mathematik · 87 Zitationen · DOI

• A posteriori error estimates for nonconforming finite element methods

  2002

  Numerische Mathematik · 86 Zitationen · DOI

• Convergence analysis of an adaptive nonconforming finite element method

  2006

  Numerische Mathematik · 85 Zitationen · DOI

• A unifying theory of a posteriori finite element error control

  2005

  Numerische Mathematik · 84 Zitationen · DOI

• Gesellschaft für angewandte Mathematik und Mechanik

  Workshop Reliable Methods and Mathematical Modeling

  other

Name

Prof. Dr. Carsten Carstensen

Titel

Prof. Dr.

Fakultät

Mathematisch-Naturwissenschaftliche Fakultät

Institut

Institut für Mathematik

Arbeitsgruppe

Numerische Behandlung von Differentialgleichungen

Telefon

+49 30 2093-45370

HU-FIS-Profil

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Zuletzt gescrapt

26.4.2026, 01:03:31