Multigrid Methods for Mortar Finite Elements

A general framework for multigrid methods for mortar finite elements

In this paper, a general framework for the analysis of multigrid methods for mortar finite elements is considered. The numerical realization is based on the algebraic saddle point formulation arising from the discretization of second order elliptic equations on nonmatching grids. Suitable discrete Lagrange multipliers on the interface guarantee weak continuity and an optimal discretization sche...

A Quasi-dual Lagrange Multiplier Space for Serendipity Mortar Finite Elements in 3d

Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained m...

Second Order Lagrange Multiplier Spaces for Mortar Finite Elements in 3D

Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained m...

Parallel linear algebra and the application to multigrid methods

We explain a general model for a parallel linear algebra. All algebraic operations and parallel extensions are defined formally, and it is shown that in this model multigrid methods on a distributed set of indices can be realized. This abstract formalization leads to an automatic realization of parallel methods for time-dependent and nonlinear partial differential equations and the solution of ...

Analysis of a Multigrid Algorithm for the Mortar Finite Element Method