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arXiv · 1610.02331

A staggered discontinuous Galerkin method for a class of nonlinear elliptic equations

Eric T. Chung·Ming Fai Lam·Chi Yeung Lam
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Abstract

In this paper, we present a staggered discontinuous Galerkin (SDG) method for a class of nonlinear elliptic equations in two dimensions. The SDG methods have some distinctive advantages, and have been successfully applied to a wide range of problems including Maxwell equations, acoustic wave equation, elastodynamics and incompressible Navier-Stokes equations. Among many advantages of the SDG methods, one can apply a local post-processing technique to the solution, and obtain superconvergence. We will analyze the stability of the method and derive a priori error estimates. We solve the resulting nonlinear system using the Newton's method, and the numerical results confirm the theoretical rates of convergence and superconvergence.

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Eric T. Chung, Ming Fai Lam, Chi Yeung Lam. 2016-10-07. A staggered discontinuous Galerkin method for a class of nonlinear elliptic equations. https://arxiv.org/abs/1610.02331

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