Title:       Overcoming corner singularities by multigrid methods

Author:      Susanne C. Brenner

Published:   SIAM Journal of Numerical Analysis
             v. 35 (1998),  1883-1892 (MR# 99f:65189)

Abstract: We consider the Poisson equation $-\Delta u = f$ with 
the homogeneous Dirichlet boundary condition on a two-dimensional 
polygonal domain $\O$.  We develop a finite element multigrid method
on quasi-uniform grids that has an order of convergence  
${\Cal{O}}(h^{m+1-\epsilon})$ 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.


 paper: SIAM Journal on Numerical Analysis




Presented at:

-Approximation and PDEs, Foundations of Computational Mathematics,
 Rio de Janeiro, Brazil, January 5--12, 1997

-Eighth Copper Mountain Conference on Multigrid Methods, 
 Copper Mountain, Colorado, April 6--11, 1997

-Third IMACS International Symposium on Iterative Methods 
 in Scientific  Computation, Jackson Hole, WY, July 9--12, 1997

-Guangzhou International Symposium on Computational Mathematics,
 Guangzhou, PRC, August 11-15, 1997 

-Innovative Finite Element Computations in Continuum Mechanics,
 15th IMACS World Congress, Berlin, Germany, August 24--29, 1997

-Imperial College, University of London, July 14, 1998

-University of Leeds, July 16, 1998

-University of Loughborough, July 17, 1998