A curved boundary treatment for discontinuous Galerkin schemes solving time dependent problems
 作者： Xiangxiong Zhang 作者单位： 1Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, United States 刊名： Journal of Computational Physics, 2016, Vol.308 , pp.153-170 来源数据库： Elsevier Journal DOI： 10.1016/j.jcp.2015.12.036 关键词： Discontinuous Galerkin;  Curved boundary;  Local discontinuous Galerkin method;  High order accuracy;  Conservation laws;  Wave equations; 原始语种摘要： Abstract(#br)For problems defined in a two-dimensional domain Ω with boundary conditions specified on a curve Γ, we consider discontinuous Galerkin (DG) schemes with high order polynomial basis functions on a geometry fitting triangular mesh. It is well known that directly imposing the given boundary conditions on a piecewise segment approximation boundary Γ h will render any finite element method to be at most second order accurate. Unless the boundary conditions can be accurately transferred from Γ to Γ h , in general curvilinear element method should be used to obtain high order accuracy. We discuss a simple boundary treatment which can be implemented as a modified DG scheme defined on triangles adjacent to Γ h . Even though integration along the curve is still necessary, integrals... over any curved element are avoided. If the domain Ω is convex, or if Ω is nonconvex and the true solutions can be smoothly extended to the exterior of Ω, the modified DG scheme is high order accurate. In these cases, numerical tests on first order and second order partial differential equations including hyperbolic systems and the scalar wave equation suggest that it is as accurate as the full curvilinear DG scheme.

• curved　弯的
• boundary　边界
• accurate　精确的
• discontinuous　不连续的
• curvilinear　曲线的
• dependent　从属的
• render　三层涂抹
• integration　集成
• piecewise　分段
• treatment　处理