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...

The dynamical investigation of two-component poroelastic media is important for practical applications. Analytic solution methods are often not available since they are too complicated for the complex governing sets of equations. For this reason, often some existing numerical methods are used. In this work results obtained with the finite element method are opposed to those obtained by Schanz u...

This paper deals with a general framework for a posteriori error estimates in boundary element methods which is specified for three examples, namely Symm's integral equation, an integral equation with a hypersingular operator, and a boundary integral equation for a transmission problem. Based on these estimates, an analog of Eriksson and Johnson's adaptive finite element method is proposed for ...

We consider scattering of a time-harmonic acoustic incident plane wave by a sound soft convex curvilinear polygon with Lipschitz boundary. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the number of degrees of freedom required to achieve a prescribed level of accuracy grows at least linearly with respect to the frequency of the incident wave. ...

This paper compares the hybrid FEM-BEM and FEM-DBCI methods for the solution of openboundary electrostatic field problems. Both methods couple a differential equation for the interior problem with an integral equation for the exterior one. The comparison shows that FEM-BEM is more accurate than FEM-DBCI but requires more computing time. PACS. 41.20.Cv Electrostatics; Poisson and Laplace equatio...

We develop a discretization scheme for the coupling of the finite volume method and the boundary element method in two dimensions, which describes, for example, the transport of a concentration in a fluid. The discrete system maintains naturally local conservation. In a bounded interior domain we approximate a diffusion convection reaction problem either by the finite volume element method or b...

In our talk, we propose an adaptive mesh-refining strategy for the cell-centered FVM based on some a posteriori error control for the quantity ‖∇T (u − Iuh)‖L2 . Here, uh ∈ P (T ) denotes the FVM approximation of u and I is a certain interpolation operator. As model example serves the Laplace equation with mixed boundary conditions, where our contributions extend a result of [NIC05]. Moreover, ...

numerical methods such as boundary element and finite element methods are widely used for the stress analysis in solid mechanics. this study presents boundary element method based on the displacement discontinuity formulation to solve general problems of interaction between hydraulic fracturing and discontinuities. the crack tip element and a higher order boundary displacement collocation techn...