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Two-sided a posteriori estimates of global and local errors for linear elliptic type boundary value problems

Hannukainen, Antti;  Korotov, Sergey — 2006

Programs and Algorithms of Numerical Mathematics

The paper is devoted to the problem of reliable control of accuracy of approximate solutions obtained in computer simulations. This task is strongly related to the so-called a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain, where such errors are too large and certain mesh refinements should be performed. Mathematical model described by a linear elliptic (reaction-diffusion) equation with mixed boundary conditions is considered....

On Synge-type angle condition for d -simplices

Antti Hannukainen;  Sergey Korotov;  Michal Křížek — 2017

Applications of Mathematics

The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in ℝ d that degenerate in some way.

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