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Vanselow, Reiner

New results concerning the DWR method for some nonconforming FEM. (English) Zbl 1274.65293

Appl. Math., Praha 57, No. 6, 551-568 (2012).
This paper deals with the dual-weighted residual (DWR) method for a posteriori error estimation in the case of a class of nonconforming finite element methods (FEMs). The method is presented using a model problem of two-dimensional Poisson equation with homogeneous Dirichlet boundary conditions. The author uses the Helmholtz decomposition and derives new error identities. These results are then applied to two particular nonconforming finite elements, and corresponding error indicators are derived.
Reviewer: Tomáš Vejchodský (Praha)

Cited in 2 Documents

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Keywords:

Poisson equation; finite element method; a posteriori error estimates; dual-weighted residual method; Helmholtz decomposition
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References:

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