针对曲域上非散度形式椭圆方程的DGFEM
A DGFEM for Nondivergence Form Elliptic Equations with Cordes Coefficients on Curved Domains
AI总结：
本文提出一种适用于Lipschitz连续域的不连续Galerkin有限元方法，扩展了原方法对凸多边形域的假设，适用于具有分段曲边的域。
摘要：
在Smears和Süli于2013年发表的SIAM J. Numer Anal. 51(4):2088-2106中，作者设计并分析了用于非散度形式椭圆偏微分方程解近似的不连续Galerkin有限元方法。结果基于计算域为凸且多边形的假设。本文扩展了该框架，允许Lipschitz连续域，具有分段曲边界。
英文摘要：
In "I. Smears, E. Süli, \emph{Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordés coefficients. SIAM J. Numer Anal., 51(4):2088-2106, 2013}" the authors designed and analysed a discontinuous Galerkin finite element method for the approximation of solutions to elliptic partial differential equations in nondivergence form. The results were proven, based on the assumption that the computational domain was convex and \emph{polytopal}. In this paper, we extend this framework, allowing for Lipschitz continuous domains with piecewise curved boundaries.
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