Singular Function Mortar Finite Element Methods

Singular Function Mortar Finite Element Methods

We consider the Poisson equation with Dirichlet boundary conditions on a polygonal domain with one reentrant corner. We introduce new nonconforming finite element discretizations based on mortar techniques and singular functions. The main idea introduced in this paper is the replacement of cut-off functions by mortar element techniques on the boundary of the domain. As advantages, the new discr...

Singular Function Enhanced Mortar Finite Element 477

We assume the function f ∈ L(Ω). We also assume the function u0 has an extension H(Ω), which we denote also by u0. We let the domain Ω to be the L-shaped domain in 2 with vertices V1 = {0, 0}, V2 = {1, 0}, V3 = {1, 1}, V4 = {−1, 1}, V5 = {−1,−1}, and V6 = {0,−1}. It is well-known that the solution u∗ of (1.1) does not necessarily belong to H(Ω) due to the nonconvexity of the domain Ω at the cor...

Domain Decomposition Capabilities for the Mortar Finite Volume Element Methods

Since the introduction of the mortar method as a coupling technique between the spectral and nite element methods see e g it has become the most important technique in domain decomposition methods for non matching grids The active research by the scienti c computation community in this eld is motivated by its exibility and great potential for large scale parallel compu tation see e g A good des...

Mortar Finite Volume Element Methods and Domain Decompositions

Mortar multiscale finite element methods for Stokes-Darcy flows

We investigate mortar multiscale numerical methods for coupled Stokes and Darcy flows with the Beavers–Joseph–Saffman interface condition. The domain is decomposed into a series of subdomains (coarse grid) of either Stokes or Darcy type. The subdomains are discretized by appropriate Stokes or Darcy finite elements. The solution is resolved locally (in each coarse element) on a fine scale, allow...