Multigrid methods for discrete elliptic problems on triangular surfaces

Abstract

We construct and analyze multigrid methods for discretized self-adjoint elliptic problems on triangular surfaces in R3. The methods involve the same weights for restriction and prolongation as in the case of planar triangulations and therefore are easy to implement. We prove logarithmic bounds of the convergence rates with constants solely depending on the ellipticity, the smoothers and on the regularity of the triangles forming the triangular surface. Our theoretical results are illustrated by numerical computations.