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

doi:10.1007/s42967-020-00102-5

摘要/Abstract

摘要： 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 diferentiation of the DG form and the target functional but using a suitable linearization of the nonlinear forms. Furthermore, we present the goaloriented anisotropic hp-mesh adaptation method for the Euler equations. The theoretical results are supported by numerical experiments.

关键词: Euler equations, Discontinuous Galerkin method, Target functional, Adjoint consistency, Anisotropic hp-mesh adaptation

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 diferentiation of the DG form and the target functional but using a suitable linearization of the nonlinear forms. Furthermore, we present the goaloriented anisotropic hp-mesh adaptation method for the Euler equations. The theoretical results are supported by numerical experiments.

Key words: Euler equations, Discontinuous Galerkin method, Target functional, Adjoint consistency, Anisotropic hp-mesh adaptation

中图分类号:

Vít Dolejší, Filip Roskovec. Goal-Oriented Anisotropic hp-Adaptive Discontinuous Galerkin Method for the Euler Equations[J]. Communications on Applied Mathematics and Computation, 2022, 4(1): 143-179.

参考文献

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