Objectives:
The project deals with the numerical solution of several types of partial differential equations (PDEs) describing various practical phenomena and problems. The aim is to develop reliable and efficient numerical methods allowing to obtain approximate solutions of PDEs under the given tolerance using a minimal number of arithmetic operations. The whole process includes the proposals and analysis of discretization schemes together with suitable solvers for the solution of arising algebraic systems, a posteriori error estimation including algebraic errors and adaptive techniques balancing various error contributions. We focus on the use of adaptive higher-order schemes which allow to reduce significantly the number of necessary degrees of freedom required for the achievement of the prescribed accuracy. The adaptive mesh refinement must also take into account the properties of the resulting algebraic systems. The expected outputs of this projects are adaptive reliable and efficient numerical methods for the solution of the considered types of PDEs.
IM leader :
Main investigator:
Dolejší Vít
IM team members:
|
Křížek Michal Kůs Pavel Papež Jan |
Rozložník Miroslav She Bangwei Šístek Jakub |
Participating institutions:
Faculty of Mathematics and Physics, Charles University, Coordinator
Institute of Mathematics, Czech Academy of Sciences
