Analysis of time discretizations for parabolic problems with application to space discretizations
Typ dokumentu
habilitační prácehabilitation thesis
Autor
Vlasák, Miloslav
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This work summarizes some of the theoretical results of the author in last ten
years, where the main area of the research was the numerical analysis for the stable
higher order time discretization methods applied on parabolic problems. The main
discretization scheme is the time discontinuous Galerkin method in combination
with the conforming finite element method or the discontinuous Galerkin method
in space. The thesis presents a priori error estimates for nonstationary singularly
perturbed convection-diffusion problems, stability results for the problems with the
domain evolving in time and a posteriori error estimates based on the equilibrated
flux reconstructions. The technique presented for a posteriori analysis in time is
applied to purely spatial problem and the quality of the recontruction is investigated
with respect to the degree of polynomial approximation.
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