2,570 research outputs found
Vektorisierte Implementierung von P1-FEM in 3D (Supervisor: M. Page, D. Praetorius)
No full textIn [Funken, Praetorius, Wissgott 2011], a vectorized Matlab
implementation of adaptive P1-FEM is given. We generalize this
approach to 3D, where emphasis is laid on the effective treatment
of newest vertex bisection in 3D
Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 1)
No full textThis paper introduces the contents of the first of two special issues associated with the 9th International Conference on Computational Methods in Applied Mathematics, which took place from August 29 to September 2, 2022 in Vienna. It comments on the topics and highlights of all twelve papers of the special issue
Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 2)
No full textThis paper introduces the contents of the second of two special issues associated with the 9th International Conference on Computational Methods in Applied Mathematics, which took place from August 29 to September 2, 2022 in Vienna. It comments on the topics and highlights of all twelve papers of the special issue
Different Strategies for the Adaptive FEM-BEM Coupling (Supervisor: M. Aurada, D. Praetorius)
No full textFor a nonlinear transmission problem with the 2D Laplacian, we
consider three different FEM-BEM coupling strategies, namely
o the symmetric coupling due to Costabel,
o the Johnson-Nedelec coupling,
o the Bielak-MacCamy coupling.
we recall the continuous and discrete formulations and collect the
mathmatical results available in the current literature. For the
symmetric coupling, we recall two adaptive strategies steered by
the residual error estimator from [Carstensen, Stephan 1995] and the
recently introduced (h-h/2)-type error estimator from [Aurada, Feischl,
Praetorius 2010]. Numerical experiments conclude the work
Energy contraction and optimal convergence of adaptive iterative linearized finite element methods
No full textWe revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [P. Heid and T. P. Wihler, Adaptive iterative linearization Galerkin methods for nonlinear problems, Math. Comp. 89 2020, 326, 2707–2734; P. Heid and T. P. Wihler, On the convergence of adaptive iterative linearized Galerkin methods, Calcolo 57 2020, Paper No. 24] satisfies an energy contraction property in the context of (abstract) strongly monotone problems. This property, in turn, is the crucial ingredient in the recent convergence analysis in [G. Gantner, A. Haberl, D. Praetorius and S. Schimanko, Rate optimality of adaptive finite element methods with respect to the overall computational costs, preprint 2020]. In particular, we deduce that adaptive iterative linearized finite element methods (AILFEMs) lead to full linear convergence with optimal algebraic rates with respect to the degrees of freedom as well as the total computational time
Rate optimality of adaptive algorithms
No full textThe overwhelming practical success of adaptive mesh-refinement in computational sciences
and engineering has recently obtained a mathematical foundation with a theory on optimal
convergence rates. This article first explains an abstract adaptive algorithm and its marking
strategy. Secondly, it elucidates the concept of optimality in nonlinear approximation theory
for a general audience. It thirdly outlines an abstract framework with fairly general hypotheses
(A1)-(A4) which imply such an optimality result. Various comments conclude this state of the
art overview.
All details and precise references are found in the open access article [Carsten Carstensen,
Michael Feischl, Marcus Page, and Dirk Praetorius: Axioms of adaptivity, Comput. Math. Appl.
67 (2014)] at http://dx.doi.org/10.1016/j.camwa.2013.12.003
http://www.eccomas.org/spacehome/1/2
Adaptive vertex-centered finite volume methods for general second-order linear elliptic partial differential equations
No full textWe prove optimal convergence rates for the discretization of a general second-order linear elliptic PDE with an adaptive vertex-centered finite volume scheme. While our prior work Erath and Praetorius [SIAM J. Numer. Anal., 54 (2016), pp. 2228-2255] was restricted to symmetric problems, the present analysis also covers non-symmetric problems and hence the important case of present convection
Adaptive vertex-centered finite volume methods for general second-order linear elliptic PDEs
No full textWe prove optimal convergence rates for the discretization of a general second-order linear elliptic PDE with an adaptive vertex-centered finite volume scheme. While our prior work Erath and Praetorius [SIAM J. Numer. Anal., 54 (2016), pp. 2228-2255] was restricted to symmetric problems, the present analysis also covers non-symmetric problems and hence the important case of present convection
Erratum to: On 2D newest vertex bisection: optimality of mesh-closure and H1-stability of L2-projection
No full textPart of the proof of Theorem 3 in [Karkulik, Pavlicek, Praetorius: Constr. Approx. 38 (2013), 213-234] is incorrect, while the result remains true
Entertainer: Pieter-Dirk Uys
No full textThis booklet celebrates the life and work of Pieter-Dirk Uys, internationally acclaimed playwright, author, role-model and one of South Africa's living treasures
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