Development of a LDG method on polytopal mesh with optimal order of convergence
Ye, Xiu 1Zhang, Shangyou 2Zhu, Peng3
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作者信息
1. Univ Arkansas Little Rock
2. Univ Delaware
3. Jiaxing Univ
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Abstract
A Local discontinuous Galerkin (LDG) finite element method on triangular mesh was introduced and analyzed in Castillo et al. (2000) for elliptic problem with suboptimal order of convergence for the flux variable. The purpose of this work is to develop a LDG finite element method on polytopal mesh that achieves optimal convergence rate for both unknowns, potential u and its gradient q. In our new LDG method, u and q are approximated by polynomials of degree k and k - 1 respectively. Optimal order of convergence are obtained for both unknowns. Numerical results in 2d and 3d are presented to confirm the theory.(C) 2022 Elsevier B.V. All rights reserved.
Key words
Finite element methods/LDG methods/WG methods/Modified WG methods/Polytopal mesh/FINITE-ELEMENT-METHOD/DISCONTINUOUS GALERKIN METHOD
NSTL
Elsevier