Grant 201/04/P021
1.1.2003 - 31.12.2006
Grantor: Czech Science Foundation
Mesh adaptivity for numerical solution of parabolic partial differential equations
We analyzed adaptive methods for numerical solution of partial differential equations. We concentrated on the hp-version of the finite element method (hp-FEM) and on the problem of hp-adaptivity. One of the studied aspects were the a posteriori error estimates. We developed a new guaranteed error estimate, which enables to compute an approximate solution with guaranteed accuracy. We also optimized the hp-FEM basis functions in order to improve the conditioning properties of the resulting matrices. Another aspect of the project was the analysis of the discrete maximum principles. We developed a simple conditions that guarantee the nonnegativity of the hp-FEM solutions. Within the project we also participated on the development of the hp-FEM software project Hermes.
Participating institutions:
Institute of Mathematics AS CR
CZ
