Multigrid analysis of finite element methods with numerical integration

Multigrid Analysis of Finite Element Methods with Numerical Integration

We analyze multigrid convergence rates when elliptic boundary value problems are discretized using finite element methods with numerical integration. The resulting discrete problem does not fall into the standard variational framework for analyzing multigrid methods since the bilinear forms on different grid levels are not suitably related to each other. We first discuss extensions of the stand...

Heterogeneous Multiscale Finite Element Method with Novel Numerical Integration Schemes

In this paper we introduce two novel numerical integration schemes, within the framework of the heterogeneous multiscale method (HMM) when finite element method is used as the macroscopic solver, to resolve the elliptic problem with multiscale coefficient. For non-self-adjoint elliptic problems, optimal convergence rate is proved for the proposed methods, which naturally yields a new strategy f...

Heterogeneous Multiscale Finite Element Method with Novel Numerical Integration Schemes

In this paper we introduce two novel numerical integration schemes, within the framework of the heterogeneous multiscale method (HMM) when finite element method is used as the macroscopic solver, to resolve the elliptic problem with multiscale coefficient. For non-self-adjoint elliptic problems, optimal convergence rate is proved for the proposed methods, which naturally yields a new strategy f...

Generic programming and algebraic multigrid for stabilized finite element methods

Multigrid on the Interface for Mortarmixed Finite Element Methods

We consider mixed nite element approximations of second order elliptic equations on domains that can be described as a union of sub-domains or blocks. We assume that the subdomain grids are locally deened and need not match across the block boundaries. Specially chosen mortar nite element spaces are introduced on the interfaces for approximating the scalar variable (pressure). The mortars also ...