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Tomáš Vejchodský 《Applications of Mathematics》2003,48(2):129-151
A posteriori error estimates for a nonlinear parabolic problem are introduced. A fully discrete scheme is studied. The space discretization is based on a concept of hierarchical finite element basis functions. The time discretization is done using singly implicit Runge-Kutta method (SIRK). The convergence of the effectivity index is proven. 相似文献
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Tomáš Vejchodský 《Central European Journal of Mathematics》2012,10(1):25-43
This paper provides an equivalent characterization of the discrete maximum principle for Galerkin solutions of general linear
elliptic problems. The characterization is formulated in terms of the discrete Green’s function and the elliptic projection
of the boundary data. This general concept is applied to the analysis of the discrete maximum principle for the higher-order
finite elements in one-dimension and to the lowest-order finite elements on simplices of arbitrary dimension. The paper surveys
the state of the art in the field of the discrete maximum principle and provides new generalizations of several results. 相似文献
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Michal Křížek Jan Němec Tomáš Vejchodský 《Advances in Computational Mathematics》2001,15(1-4):219-236
We propose and examine the primal and dual finite element method for solving an axially symmetric elliptic problem with mixed boundary conditions. We derive an a posteriori error estimate and generalize the method used for a nonlinear elliptic problem. Finally, an a posteriori error estimate for a nonlinear parabolic problem based on the concept of hierarchical finite element basis functions is introduced. 相似文献
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