The hp nonconforming mesh refinement in discontinuous Galerkin finite element method based on Zienkiewicz-Zhu error estimation

  • Jan Jaśkowiec

Abstract

This paper deals with hp-type adaptation in the discontinuous Galerkin (DG) method. The DG method is formulated in this paper with a non-zero mesh skeleton width, which leads to a version of the method called in this paper the interface discontinuous Galerkin (IDG) method. In this formulation, the mesh skeleton has a finite volume and special finite elements are used for discretization. The skeleton spatial calculations are performed using the finite difference or mid-values formulas which are based on the shape functions of the neighbouring finite elements. The Dirichlet boundary conditions are applied using a non-zero width of the material between the outer boundary and a finite element aligned with the boundary. Next, the paper discusses the mesh refinement of hp type. In the IDG method, the mesh does not have to be conforming. The Zienkiewicz-Zhu (ZZ) error indicator is adapted in the IDG method for the purpose of mesh refinement. The paper is illustrated with two-dimensional examples, in which the mesh refinement for an elliptic problem is performed.

Keywords

discontinuous Galerkin method, hp refinement, Zienkiewicz-Zhu error estimation,
Published
Jan 25, 2017
How to Cite
JAŚKOWIEC, Jan. The hp nonconforming mesh refinement in discontinuous Galerkin finite element method based on Zienkiewicz-Zhu error estimation. Computer Assisted Methods in Engineering and Science, [S.l.], v. 23, n. 1, p. 43-67, jan. 2017. ISSN 2299-3649. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/5>. Date accessed: 12 apr. 2021.
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Articles