A goal-oriented anisotropic hp-mesh adaptation method for linear convection–diffusion–reaction problems. (1st November 2019)

• Record Type: Journal Article
• Authors: Bartoš, Ondřej; Dolejší, Vít; May, Georg; Rangarajan, Ajay; Roskovec, Filip
• Is Part Of: Computers & mathematics with applications. Volume 78:issue 9(2019)
• Page Start: 2973
• Page End: 2993
• Publication Date: 2019-11-01
• Subjects: Goal-oriented error estimates -- DWR method -- hp-methods -- Anisotropic mesh adaptation -- Mesh elements optimization; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.03.046
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We deal with the numerical solution of linear convection–diffusion–reaction equations using the h p -variant of the discontinuous Galerkin method on triangular grids. We develop a mesh adaptive algorithm which modifies the size and shape of mesh elements and the corresponding polynomial approximation degrees in order to decrease the error in a target functional under the given tolerance. We recall some theoretical results and describe in detail several technical aspects of this approach. Numerical experiments demonstrating the accuracy, efficiency and robustness of the algorithm are presented.