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Article

Keywords:
nonconforming finite elements; dual-weighted residual method; a posteriori error estimate; Poisson equation; finite element method; Helmholtz decomposition
Summary:
This paper presents a unified framework for the dual-weighted residual (DWR) method for a class of nonconforming FEM. Our approach is based on a modification of the dual problem and uses various ideas from literature which are combined in a new manner. The results are new error identities for some nonconforming FEM. Additionally, a posteriori error estimates with respect to the discrete $H^1$-seminorm are derived.
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