Showing papers by "Susanne C. Brenner published in 1998"
TL;DR: A finite element multigrid method on quasi-uniform grids that obtains convergence in the $H^1(\O)$ norm for any positive $\epsilon$ when f is in H^m(\O), which can be generalized to other equations and other boundary conditions.
Abstract: We consider the Poisson equation $-\Delta u = f$ with homogeneous Dirichlet boundary condition on a two-dimensional polygonal domain $\O$. We develop a finite element multigrid method on quasi-uniform grids that obtains ${\cal{O}}(h^{m+1-\epsilon})$ convergence in the $H^1(\O)$ norm for any positive $\epsilon$ when $f \in H^m(\O)$. The cost of the method is proportional to the number of elements in the triangulation. The results of this paper can be generalized to other equations and other boundary conditions.
18 citations