Goal-Oriented Anisotropic hp-Adaptive Discontinuous Galerkin Method for the Euler Equations

Vít Dolejší; Filip Roskovec

doi:10.1007/s42967-020-00102-5

Communications on Applied Mathematics and Computation ›› 2021, Vol. 4 ›› Issue (1) : 143 -179. DOI: 10.1007/s42967-020-00102-5

Original Paper

Goal-Oriented Anisotropic hp-Adaptive Discontinuous Galerkin Method for the Euler Equations

Vít Dolejší ¹^,a
, Filip Roskovec ¹

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Abstract

We deal with the numerical solution of the compressible Euler equations with the aid of the discontinuous Galerkin (DG) method with focus on the goal-oriented error estimates and adaptivity. We analyse the adjoint consistency of the DG scheme where the adjoint problem is not formulated by the differentiation of the DG form and the target functional but using a suitable linearization of the nonlinear forms. Furthermore, we present the goal-oriented anisotropic hp-mesh adaptation method for the Euler equations. The theoretical results are supported by numerical experiments.

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Vít Dolejší, Filip Roskovec. Goal-Oriented Anisotropic hp-Adaptive Discontinuous Galerkin Method for the Euler Equations. Communications on Applied Mathematics and Computation, 2021, 4(1): 143-179 DOI:10.1007/s42967-020-00102-5