HIGH ORDER DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS ON SURFACES
HIGH ORDER DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS ON SURFACES
复制标题
DOI：
10.1137/140957172
复制
发表时间：
2015-01-01
影响因子：
2.9
通讯作者：
Verani, Marco
中科院分区：
文献类型：
--
作者：
Antonietti, Paola F.;Dedner, Andreas;Verani, Marco
我们在R-3中隐式定义的表面上得出并分析了高阶不连续的Galerkin方法，以解决二阶椭圆问题。这是通过仔细适应[D. N. Arnold等人，Siam J. Numer。肛门，39（2002），第1749-1779页]，在近似光滑表面的三角形表面上。我们证明了A（网格依赖性）能量和L-2规范的最佳误差估计。还提出了验证我们的理论估计值的数值结果。
We derive and analyze high order discontinuous Galerkin methods for second order elliptic problems on implicitly defined surfaces in R-3. This is done by carefully adapting the unified discontinuous Galerkin framework of [D. N. Arnold et al., SIAM J. Numer. Anal., 39 (2002), pp. 1749-1779] on a triangulated surface approximating the smooth surface. We prove optimal error estimates in both a (mesh dependent) energy and L-2 norms. Numerical results validating our theoretical estimates are also presented.