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