Optimum error estimates for finite-difference methods
M. N. Spijker (1974)
Acta Universitatis Carolinae. Mathematica et Physica
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Optimum error estimates for finite-difference methods
Minimization of functional majorant in a posteriori error analysis based on (div) multigrid-preconditioned CG method.
Valdman, Jan (2009)
Advances in Numerical Analysis
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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.
A posteriori error estimation and adaptivity in the method of lines with mixed finite elements
Jan Brandts (1999)
Applications of Mathematics
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We will investigate the possibility to use superconvergence results for the mixed finite element discretizations of some time-dependent partial differential equations in the construction of a posteriori error estimators. Since essentially the same approach can be followed in two space dimensions, we will, for simplicity, consider a model problem in one space dimension.