A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, and the condition that the shape functions depend only on the node positions. Furthermore, the method proposed also shares several of the advantages of the Finite Element Method such as: (a) the simplicity of the shape functi...

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that ...

The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations. However, the generality of the framework provided by the finite element method is seldom reflected in implementations (realizations), which are often specializ...

We develop an adaptive nite element algorithm for reactive ow simulations. The underlying equations are the Navier-Stokes equations for low-Mach-number ows and an additional system of convection-diiusion-reaction equations for the chemical species. Especially in combustion problems the reaction terms are very stii and nonlinear. This set of equations represents a complicated system of PDEs whic...

The goal of this paper is to generalize the BEM-based FEM for second order elliptic boundary value problems to three space dimensions with the emphasis on polyhedral meshes with polygonal faces, where even nonconvex elements are allowed. Due to an implicit definition of the trial functions, the strategy yields conforming approximations and is very flexible with respect to the meshes. Thus, it g...

In this paper we propose and analyze some new methods for coupling mixed finite element and boundary element methods for the model problem of the Laplace equation in free space or in the exterior of a bounded domain. As opposed to the existing methods, which use the complete matrix of operators of the Calderón projector to obtain a symmetric coupled system, we propose methods with only one inte...

The purpose of this paper is to test the applicability of a fast boundary element method in the context of geoid computations of the gravity. The fast multipole method is the method of choice due to the its advantageous property of a fast evaluation in the post-processing. Several sets of trianglar meshes for the approximation of the unit sphere and several modifications of the prediscribed dat...

The aim of medical image registration is to bring different images into the best possible spatial correspondence in order to obtain complementary information for clinical applications. When using physically-based techniques for image registration the transformation of images is typically obtained as the solution of partial differential equations of continuum mechanics. Because of the complexity...

The convergence analysis of multigrid methods for boundary element equations arising from negative-order pseudo-differential operators is quite different from the usual finite element multigrid analysis for elliptic partial differential equations. In this paper, we study the convergence of geometric multigrid methods for solving large-scale, data-sparse boundary element equations arising from t...