Prof. Dr. Carsten Carstensen

Profil

Zusammenfassung

Carsten Carstensen entwickelt mathematische Methoden und Algorithmen zur numerischen Simulation komplexer mechanischer Probleme, insbesondere in der Festkörpermechanik und Plastizität. Seine Expertise liegt in adaptiven Finite-Elemente-Verfahren und verlässlichen Fehlerabschätzungen, die es ermöglichen, Rechenergebnisse zu kontrollieren und Gitterverfeinerungen automatisiert zu steuern. Diese Methoden sind für die industrielle Simulation von Werkzeugbearbeitung, Umformvorgängen und anderen nichtlinearen Strukturproblemen praktisch relevant.

Skills

Name

Prof. Dr. Carsten Carstensen

Titel

Prof. Dr.

Fakultät

Mathematisch-Naturwissenschaftliche Fakultät

Institut

Institut für Mathematik

Arbeitsgruppe

Numerische Behandlung von Differentialgleichungen

E-Mail

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HU-FIS-Profil

Quelle ↗

Zuletzt gescrapt

27.6.2026, 01:04:28

• 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

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

  2001

  Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 357 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 · 278 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 · 236 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.

• Gesellschaft für angewandte Mathematik und Mechanik

  Workshop Reliable Methods and Mathematical Modeling

  other