Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
Abstract
Using the Galerkin FEM to solve the Helmholtz equation, the error of the corresponding solution differs from the error of the best approximation substantially, and this effect increases with higher wave numbers k. In the one dimensional case, we will define a stabilized variant of the FEM which fits in the setting of the generalized FEM (GFEM). This variant will produce a FE-solution being very dose to the best approximation, and we can prove quasioptimal error estimates without any pollution effect. This situation changes essentially in the higher dimensional case. We will show that for every GFEM there exists a domain and a solution of the Helmholtz equation which cannot be approximated without any pollution. Numerical examples will illustrate the improvement of the stabilized FEM compared with the Galerkin FEM
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1994
- Accession Number
- ADA282585
Entities
People
- Ivo M. Babuska
- Stefan A. Sauter
Organizations
- University of Maryland