A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of userdefined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impo...

The effect of the boundary conditions on the global dynamics of cellular neural networks (CNNs) is investigated. As a case study one dimensional template CNNs are considered. It is shown that if off-diagonal template elements have the same sign (i.e. the CNN is completely stable), then the qualitative dynamics is not influenced by the boundary conditions. If the off-diagonal template elements h...

In this paper, we propose a simplified pollution adaptive mesh generation algorithm using singular elements. The algorithm based on the element pollution error indicator concentrate on boundary nodes. The automatic mesh generation method is fo llowed by either a node-relocation or a node-insertion method. The boundary node relocation phase is introduced to reduce pollution error estimates witho...

Finite element (FEM) and boundary element (BEM) methods have been used for a long time for the numerical simulation of acoustic problems. The development presented in this paper deals with a general procedure for coupling acoustic finite elements with acoustic boundary elements in order to solve efficiently acoustic problems involving non homogeneous fluids. Emphasis is made on problems where f...