Name
Title | ||
|---|---|---|
Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions |
Abstract | ||
|---|---|---|
A rigorous convergence theory for Galerkin methods for a model Helmholtz problem in R-d, d is an element of {1, 2, 3} is presented. General conditions on the approximation properties of the approximation space are stated that ensure quasi-optimality of the method. As an application of the general theory, a full error analysis of the classical hp-version of the finite element method (hp-FEM) is presented for the model problem where the dependence on the mesh width h, the approximation order p, and the wave number k is given explicitly. In particular, it is shown that quasi-optimality is obtained under the conditions that kh/p is sufficiently small and the polynomial degree p is at least O(log k). |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1090/S0025-5718-10-02362-8 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
Helmholtz equation at high wave number,stability,convergence,hp-finite elements | Boundary value problem,Mathematical analysis,Galerkin method,Helmholtz free energy,Degree of a polynomial,Finite element method,Helmholtz equation,Neumann boundary condition,Numerical analysis,Mathematics | Journal |
Volume | Issue | ISSN |
79 | 272 | 0025-5718 |
Citations | PageRank | References |
24 | 1.42 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jens Markus Melenk | 1 | 133 | 24.18 |
| Stefan Sauter | 2 | 87 | 6.98 |