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

作     者：Vít Dolejší Filip Roskovec 

作者机构：Faculty of Mathematics and PhysicsCharles UniversitySokolovská8318675 PragueCzech Republic 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2022年第4卷第1期

页      面：143-179页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Grant no.20-01074S of the Czech Science Foundation. 

主　　题：Euler equations Discontinuous Galerkin method Target functional Adjoint consistency Anisotropic hp-mesh adaptation 

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 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.