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A posteriori error estimates for numerical solution of convection-difusion problems
Šebestová, Ivana ; Dolejší, Vít (advisor) ; Sváček, Petr (referee) ; Brandts, Jan (referee)
This thesis is concerned with several issues of a posteriori error estimates for linear problems. In its first part error estimates for the heat conduction equation discretized by the backward Euler method in time and discontinuous Galerkin method in space are derived. In the second part guaranteed and locally efficient error estimates involving algebraic error for Poisson equation discretized by the discontinuous Galerkin method are derived. The technique is based on the flux reconstruction where meshes with hanging nodes and variable polynomial degree are allowed. An adaptive strategy combining both adaptive mesh refinement and stopping criteria for iterative algebraic solvers is proposed. In the last part a numerical method for computing guaranteed lower and upper bounds of principal eigenvalues of symmetric linear elliptic differential operators is presented. 1
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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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A posteriori error estimates for numerical solution of convection-difusion problems
Šebestová, Ivana ; Dolejší, Vít (advisor) ; Sváček, Petr (referee) ; Brandts, Jan (referee)
This thesis is concerned with several issues of a posteriori error estimates for linear problems. In its first part error estimates for the heat conduction equation discretized by the backward Euler method in time and discontinuous Galerkin method in space are derived. In the second part guaranteed and locally efficient error estimates involving algebraic error for Poisson equation discretized by the discontinuous Galerkin method are derived. The technique is based on the flux reconstruction where meshes with hanging nodes and variable polynomial degree are allowed. An adaptive strategy combining both adaptive mesh refinement and stopping criteria for iterative algebraic solvers is proposed. In the last part a numerical method for computing guaranteed lower and upper bounds of principal eigenvalues of symmetric linear elliptic differential operators is presented. 1
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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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