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- W3100456168 abstract "This article lays a mathematical foundation for goal-oriented adaptive mesh refinement and a posteriori error estimation with discontinuous Petrov--Galerkin (DPG) finite element methods. A goal-oriented adaptive mesh refinement procedure is proposed which requires the construction of refinement indicators for both a primal problem and a dual problem. The primal problem can be associated to a standard DPG method and the dual problem can be associated to a a new dual method. This new method has the same coefficient matrix as the associated DPG method but has a different load. We refer to this new finite element method as a DPG* method. For DPG methods, the current theory of a posteriori error estimation is reviewed and the reliability estimate in [C. Carstensen, L. Demkowicz, and J. Gopalakrishnan, SIAM J. Numer. Anal., 52 (2014), pp. 1335--1353, Theorem 2.1] is improved on. For DPG* methods, a novel class of refinement indicators are derived and analyzed. The article closes with numerical experiments with Poisson's boundary value problem in a three-dimensional domain." @default.
- W3100456168 created "2020-11-23" @default.
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- W3100456168 date "2019-01-01" @default.
- W3100456168 modified "2023-10-18" @default.
- W3100456168 title "Goal-Oriented Adaptive Mesh Refinement for Discontinuous Petrov--Galerkin Methods" @default.
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- W3100456168 doi "https://doi.org/10.1137/18m1181754" @default.
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