Convergence Of Galerkin Method Research Articles

Nonsymmetric coupling of BEM and mixed FEM on polyhedral interfaces

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 Calderon projector to obtain a symmetric coupled system, we propose methods with only one integral equation. The system can be considered as a further generalization of the Johnson-Nedelec coupling of BEM—FEM to the case of mixed formulations in the bounded domain. Using some recent analytical tools we are able to prove stability and convergence of Galerkin methods with very general conditions on the discrete spaces and no restriction relating the finite and boundary element spaces. This can be done for general Lipschitz interfaces and in particular, the coupling boundary can be taken to be a Lipschitz polyhedron. Both the indirect and the direct approaches for the boundary integral formulation are explored.

Estimates for the Rate of Convergence of the Galerkin Method for Abstract Hyperbolic Equations

We study the rate of convergence of the semidiscrete Galerkin method for linear hyperbolic equations in a Hilbert space. We establish asymptotic estimates for the error arising as a result of the arbitrariness in the choice of subspaces in which the approximation problems are solved.

Convergence of a Galerkin method for 2-D discontinuous Euler flows

We prove the convergence of a discontinuous Galerkin method approximating the 2-D incompressible Euler equations with discontinuous initial vorticity: !0 2 L 2 (Ω). Furthermore, when !0 2 L ∞ (Ω), the whole sequence is shown to be strongly convergent. This is the first convergence result in numerical approximations of this general class of discontinuous flows. Some important flows such as vortex patches belong to this class. c 2000 John Wiley & Sons, Inc.

Projektionsverfahren f�r Randwertaufgaben mit nichtlinearen Randbedingungen

In this paper we prove the convergence of projection methods for the equationLx=Gx with a linear operatorL and a Frechet-differentiable OperatorG. This theorem is used to establish the convergence of Galerkin's method and certain projection methods with splines for boundary value problems with nonlinear boundary conditions.