The Convergence of V-Cycle Multigrid Algorithms for Axisymmetric Laplace and Maxwell Equations

摘要: We investigate some simple finite element discretizations for the axisymmetric Laplace equation and azimuthal component of Maxwell equations as well multigrid algorithms these discretizations. Our analysis is targeted at model problems our main result that standard V-cycle with point smoothing converges a rate independent number unknowns. This contrary to suggestions in existing literature line relaxations semicoarsening are needed overcome difficulties caused by singularities problems. proceeds applying known regularity based theory. In order apply this theory, we prove results certain weighted Sobolev spaces. These, together new error estimates norms, ingredients analysis.