Goal-oriented \(hp\)-adaptivity for elliptic problems. (English) Zbl 1044.65082

Summary: We propose and test a fully automatic, goal-oriented \(hp\)-adaptive strategy for elliptic problems. The method combines two techniques: the standard goal-oriented adaptivity based on a simultaneous solution of a dual problem, and a recently proposed \(hp\)-strategy based on minimizing the projection-based interpolation error of a reference solution. The proposed strategy is illustrated with two numerical examples: Laplace equation in L-shape domain, and an axisymmetric Maxwell problem involving radiation of a loop antenna wrapped around a metallic cylinder into a conductive medium.


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35Q60 PDEs in connection with optics and electromagnetic theory
78A40 Waves and radiation in optics and electromagnetic theory
78A50 Antennas, waveguides in optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
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