Abstract
We develop a new technique which, for the given smooth function, generates the anisotropic triangular grid and the corresponding polynomial approximation degrees based on the minimization of the interpolation error in the broken H 1-seminorm. This technique can be employed for the numerical solution of boundary value problems with the aid of finite element methods. We present the theoretical background of this approach and show several numerical examples demonstrating the efficiency of the proposed anisotropic adaptive strategy in comparison with other adaptive approaches.
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Cordially dedicated to prof. Ivo Babuška, the founder of hp-methods
The research of V.Dolejši has been supported by Grant No. 13-00522S of the Czech Science Foundation. The author acknowledges also the membership in the Nečas Center for Mathematical Modeling ncmm@karlin.mff.cuni.cz.
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Dolejší, V. Anisotropic hp-adaptive method based on interpolation error estimates in the H 1-seminorm. Appl Math 60, 597–616 (2015). https://doi.org/10.1007/s10492-015-0113-7
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DOI: https://doi.org/10.1007/s10492-015-0113-7