solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看5372次
A Stable Cut Finite Element Method for Partial Differential Equations on Surfaces: The Helmholtz-Beltrami Operator. (arXiv:1810.04217v1 [math.NA])
来源于:arXiv
We consider solving the surface Helmholtz equation on a smooth two
dimensional surface embedded into a three dimensional space meshed with
tetrahedra. The mesh does not respect the surface and thus the surface cuts
through the elements. We consider a Galerkin method based on using the
restrictions of continuous piecewise linears defined on the tetrahedra to the
surface as trial and test functions.Using a stabilized method combining
Galerkin least squares stabilization and a penalty on the gradient jumps we
obtain stability of the discrete formulation under the condition $h k < C$,
where $h$ denotes the mesh size, $k$ the wave number and $C$ a constant
depending mainly on the surface curvature $\kappa$, but not on the surface/mesh
intersection. Optimal error estimates in the $H^1$ and $L^2$-norms follow. 查看全文>>