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Displaying similar documents to “A posteriori error estimates for parabolic differential systems solved by the finite element method of lines”

Grid adjustment based on a posteriori error estimators

Karel Segeth (1993)

Applications of Mathematics

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The adjustment of one-dimensional space grid for a parabolic partial differential equation solved by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. A statement on the rate of convergence of the approximation of error by estimator to the error in the case of a system of parabolic equations is presented.

Adapting meshes and time-steps for phase change problems

Ricardo H. Nochetto, Alfred Schmidt, Claudio Verdi (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We address the numerical approximation of the two-phase Stefan problem and discuss an adaptive finite element method based on rigorous a posteriori error estimation and refinement/coarsening. We also investigate how to restrict coarsening for the resulting method to be stable and convergent. We review implementation issues associated with bisection and conclude with simulations of a persistent corner singularity, for which adaptivity is an essential tool.