Journal article
Finite element recovery techniques for local quantities of linear problems using fundamental solutions
Publication Details
Authors: | Grätsch, T.; Hartmann, F. |
Publication year: | 2003 |
Journal: | Computational Mechanics |
Pages range : | 15-21 |
Volume number: | 33 |
ISSN: | 0178-7675 |
Abstract
We show that local quantities of interest such as displacements or stresses of a FE-solution can be calculated with improved accuracy if fundamental solutions are employed. The approach is based on Betti's theorem and an integral representation of the local quantities via Green's function. The unknown Green's function is split into a regular part and a fundamental solution so that only the regular part must be approximated on the finite element ansatz space. Some numerical studies for linear elasticity will illustrate our approach.
We show that local quantities of interest such as displacements or stresses of a FE-solution can be calculated with improved accuracy if fundamental solutions are employed. The approach is based on Betti's theorem and an integral representation of the local quantities via Green's function. The unknown Green's function is split into a regular part and a fundamental solution so that only the regular part must be approximated on the finite element ansatz space. Some numerical studies for linear elasticity will illustrate our approach.
