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Grant P201/04/P021     1.1.2003 - 31.12.2006
Grantor: Grant Agency of Czech Republic (GACR)

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.

 Main investigator:

Vejchodský Tomáš