On the Convergence of Adaptive Nonconforming Finite Element Methods for a Class of Convex Variational Problems

DOI10.1137/090781073zbMath1232.49034OpenAlexW2057794497MaRDI QIDQ3091804

Christoph Ortner, Dirk Praetorius

Publication date: 14 September 2011

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://wrap.warwick.ac.uk/43788/1/WRAP_2011-SINUM_ANCFEM.pdf

zbMATH Keywords

calculus of variationsCrouzeix-Raviart finite element methodLavrentiev phenomenonconvergence of adaptive finite element methods

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Methods involving semicontinuity and convergence; relaxation (49J45) Discrete approximations in optimal control (49M25)

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Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap ⋮ Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice ⋮ Convergent adaptive hybrid higher-order schemes for convex minimization ⋮ Crouzeix-Raviart approximation of the total variation on simplicial meshes ⋮ Approximating the total variation with finite differences or finite elements ⋮ On the Sobolev and $L^p$-Stability of the $L^2$-Projection ⋮ AΓ-Convergence Result for the Upper Bound Limit Analysis of Plates ⋮ Unstabilized Hybrid High-order Method for a Class of Degenerate Convex Minimization Problems ⋮ Nonconforming FEMs for an Optimal Design Problem

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