Analysis of the discontinuous Galerkin method for elliptic problems on surfaces

被引:32
作者
Dedner, Andreas
Madhavan, Pravin [1 ]
Stinner, Bjoern
机构
[1] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England
基金
英国工程与自然科学研究理事会;
关键词
discontinuous Galerkin; interior penalty; surface partial differential equations; error analysis; GENERIC GRID INTERFACE; FINITE-ELEMENTS; PARALLEL;
D O I
10.1093/imanum/drs033
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We extend the discontinuous Galerkin framework to a linear second-order elliptic problem on a compact smooth connected and oriented surface in R-3. An interior penalty (IP) method is introduced on a discrete surface and we derive a priori error estimates by relating the latter to the original surface via the lift introduced in Dziuk (1988). The estimates suggest that the geometric error terms arising from the surface discretization do not affect the overall convergence rate of the IP method when using linear ansatz functions. This is then verified numerically for a number of test problems. An intricate issue is the approximation of the surface conormal required in the IP formulation, choices of which are investigated numerically. Furthermore, we present a generic implementation of test problems on surfaces.
引用
收藏
页码:952 / 973
页数:22
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