Weißer, Steffen; Wick, Thomas The dual-weighted residual estimator realized on polygonal meshes. (English) Zbl 1422.65417 Comput. Methods Appl. Math. 18, No. 4, 753-776 (2018). The paper is concerned with the derivation of a goal-oriented error estimator. The model problem considered is the Poisson equation on a two-dimensional polygonal domain equipped with mixed Dirichlet-Neumann boundary conditions. The equation is discretized by the BEM-based finite element method with a polygonal mesh. The estimator is derived using the dual-weighted residual method with two approaches to localization: a classical approach and a variational approach employing the partition of unity. The great advantage of the proposed method is that it uses approximation on only one element and does not require higher-order global approximation or local higher-order approximation on patched meshes. The efficiency and applicability of the method are illustrated on numerical examples with various domains, boundary conditions, and goal functionals. Reviewer: Dana Černá (Liberec) Cited in 11 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N38 Boundary element methods for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs Keywords:BEM-based FEM; polygonal finite elements; goal-oriented a posteriori error estimation; dual-weighted residual estimator; partition-of-unity PDFBibTeX XMLCite \textit{S. Weißer} and \textit{T. Wick}, Comput. Methods Appl. Math. 18, No. 4, 753--776 (2018; Zbl 1422.65417) Full Text: DOI References: [1] M. Ainsworth and J. T. Oden, A posteriori error estimation in finite element analysis, Comput. Methods Appl. Mech. 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