Abstract
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement algorithms to improve the convergence of finite element approximation. The proposed algorithm is simple, explicit, and requires less geometric conditions on the mesh and on the domain. Then, we develop interpolation error estimates in suitable weighted spaces for the anisotropic mesh. These estimates can be used to design optimal finite element methods approximating singular solutions. We report numerical test results to validate the method.
Connections
Explore this paper’s authors, topics and related work.
Building this map preview
BZPEER is loading the nearby papers, people, topics and institutions for this page.
Reviews 0
Write a review
No reviews yet.
Discussion 0
Add a comment
No comments yet.