APPLICATIONS OF MATHEMATICS, Vol. 48, No. 2, pp. 129-151, 2003

Fully discrete error estimation by the method
of lines for a nonlinear parabolic problem

Tomas Vejchodsky

Tomas Vejchodsky, Mathematical Institute of the Academy of Sciences of the Czech Republic, Zitna 25, CZ-115 67 Praha 1, Czech Republic, e-mail:
vejchod@math.cas.cz

Abstract: 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.

Keywords: a posteriori error estimates, finite elements, nonlinear parabolic problems, effectivity index, singly implicit Runge-Kutta methods (SIRK)

Classification (MSC 2000): 65M60, 65M20, 65M15

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