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A posteriori error estimates of the discontinuous Galerkin method for convection-diffusion equations
 Šebestová, Ivana
Title: A posteriori error estimates of the discontinuous Galerkin method for convection- diffusion equations Author: Ivana Šebestová Department: Department of Numerical Mathematics Supervisor: Doc. RNDr. Dolejší Vít, Ph.D., DSc. Supervisor's e-mail address: dolejsi@karlin.mff.cuni.cz Abstract: The thesis deals with a posteriori error estimates of the disconti- nuous Galerkin aproximations of diffusion problems. It has two main parts. In the first one we describe different approaches leading to a posteriori error estimate for the Poisson equation with mixed boundary conditions. The se- cond one is concerned with a heat equation discretized by the backward Euler scheme in time. We derive a posteriori error estimator which provides the error upper bound. Keywords: Discontinuous Galerkin method, a posteriori error estimates, Helmholtz decomposition, Galerkin orthogonality principle, duality principle
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