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GACR Project 2020-22
Abstract
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.