Discontinuous Galerkin methods for semilinear elliptic boundary value problem

2021/01/26 by Jiajun Zhan, Zhan, Jiajun, Liuqiang Zhong +3
Engineering · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Electromagnetic Simulation and Numerical Methods

paper · pdf · doi:10.48550/arxiv.2101.10664

Abstract

A discontinuous Galerkin (DG) scheme for solving semilinear elliptic problem is developed and analyzed in this paper. The DG finite element discretizations are established, and the corresponding existence and uniqueness theorem is proved by using Brouwer's fixed point method. Some optimal priori error estimates under both DG norm and L² norm are presented. Numerical results are also shown to confirm the efficiency of the proposed approach.

Citations

• A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier–Stokes Equations
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

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