ANALYSIS OF V-CYCLE MULTIGRID ALGORITHMS FOR FORMS DEFINED BY NUMERICAL QUADRATURE

The authors describe and analyze certain V-cycle multigird algorithms with forms defined by numerical quadrature applied to the approximatio n of symmetric second-order elliptic boundary value problems. This app roach can be used for the efficient solution of finite element systems resulting from numerical quadrature as well as systems arising from f inite difference discretizations. The results are based on a regularit y free theory and hence apply to meshes with local grid refinement as well as the quasi-uniform case. It is shown that uniform (independent of the number of levels) convergence rates often hold for appropriatel y defined V-cycle algorithms with as few as one smoothing per grid. Th ese results bold even on applications without full elliptic regularity , e.g., a domain in R2 with a crack.