A cut discontinuous Galerkin method for the Laplace-Beltrami operator
A cut discontinuous Galerkin method for the Laplace-Beltrami operator
复制标题
Laplace-Beltrami算子的截断间断Galerkin方法
DOI：
10.1093/imanum/drv068
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发表时间：
2017-01-01
影响因子：
2.1
通讯作者：
Massing, Andre
中科院分区：
文献类型：
--
作者：
Burman, Erik;Hansbo, Peter;Massing, Andre
We develop a discontinuous cut finite element method for the Laplace-Beltrami operator on a hypersurface embedded in R-d. The method is constructed by using a discontinuous piecewise linear finite element space defined on a background mesh in R-d. The surface is approximated by a continuous piecewise linear surface that cuts through the background mesh in an arbitrary fashion. Then, a discontinuous Galerkin method is formulated on the discrete surface and in order to obtain coercivity, certain stabilization terms are added on the faces between neighbouring elements that provide control of the discontinuity as well as the jump in the gradient. We derive optimal a priori error and condition number estimates which are independent of the positioning of the surface in the background mesh. Finally, we present numerical examples confirming our theoretical results.
