A posteriori error estimate in the finite element method.(Czech)Zbl 1265.74084

By means of the example of the Dirichlet problem to the equation $$-\Delta u=f$$, the author explains how to define a generalized solution of the problem, how to find a discrete model by the finite element method and how to deduce a posteriori error estimates. Moreover, several types of the a posteriori error estimates are presented.

MSC:

 74S05 Finite element methods applied to problems in solid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation