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Goal-oriented adaptive finite element methods for elliptic problems revisited. (English) Zbl 1316.65098
Summary: A goal-oriented a posteriori error estimation of an output functional for elliptic problems is presented. Continuous finite element approximations are used in quadrilateral and triangular meshes. The algorithm is similar to the classical dual-weighted error estimation, however the dual weight contains solutions of the proposed patch problems. The patch problems are introduced to apply Clément and Scott-Zhang type interpolation operators to estimate point values with the finite element polynomials. The algorithm is shown to be reliable, efficient and convergent.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
deal.ii; DOLFIN; Unicorn
Full Text: DOI
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