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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Discontinuous Galerkin method for the solution of boundary-value problems in non-smooth domains
 Bartoš, Ondřej ; Feistauer, Miloslav (advisor) ; Dolejší, Vít (referee)
This thesis is concerned with the analysis of the finite element method and the discontinuous Galerkin method for the numerical solution of an elliptic boundary value problem with a nonlinear Newton boundary condition in a two-dimensional polygonal domain. The weak solution loses regularity in a neighbourhood of boundary singularities, which may be at corners or at roots of the weak solution on edges. The main attention is paid to the study of error estimates. It turns out that the order of convergence is not dampened by the nonlinearity, if the weak solution is nonzero on a large part of the boundary. If the weak solution is zero on the whole boundary, the nonlinearity only slows down the convergence of the function values but not the convergence of the gradient. The same analysis is carried out for approximate solutions obtained with numerical integration. The theoretical results are verified by numerical experiments. 1
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Numerická kvadratura vyššího řádu ve 2D a 3D
 Segeth, Karel ; Šolín, P. ; Doležel, I.
The construction of higher-order Gauss quadrature rules in 2D and 3D is it considered. Many open questions are related to the desing of (symmetric) formulae with minimum number of points. After outlining some of the state-of-the- art knowledge and open problems in contemporary numerical quadrature related to finite element methods, we present and discuss several techniques which can (and should) be used where the current knowledge of Gaussian quadrature rules is not sufficient.
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