论文标题
弯曲域上广义的罗宾边界价值问题的等载体有限元分析
Isoparametric finite element analysis of a generalized Robin boundary value problem on curved domains
论文作者
论文摘要
我们研究了椭圆形偏微分方程的离散化，该方程在具有光滑边界的二维或三维结构域上构成，并具有广义的robin边界条件，该条件涉及边界表面上的拉普拉斯 - 贝特拉米操作员。边界用分段多项式面近似，我们使用任意顺序的等式有限元进行离散化。我们在$ l^2 $ - 和$ h^1 $ -NOMM中为此不合格的有限元方法提供了最佳订购错误界限。数值示例说明了理论结果。
We study the discretization of an elliptic partial differential equation, posed on a two- or three-dimensional domain with smooth boundary, endowed with a generalized Robin boundary condition which involves the Laplace-Beltrami operator on the boundary surface. The boundary is approximated with piecewise polynomial faces and we use isoparametric finite elements of arbitrary order for the discretization. We derive optimal-order error bounds for this non-conforming finite element method in both $L^2$- and $H^1$-norm. Numerical examples illustrate the theoretical results.
