Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations

2022/11/11 by Sebastian Franz, Franz, Sebastian, Natalia Kopteva +1 · 1 citation
Mathematics · Engineering · #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.2211.06272

Abstract

Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [7]. We improve the earlier time stepping algorithm based on this theory, and specifically address its stable and efficient implementation in the context of high-order methods. The considered methods include an L1-2 method and continuous collocation methods of arbitrary order, for which adaptive temporal meshes are shown to yield optimal convergence rates in the presence of solution singularities.

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• Numerical Reconstruction and Analysis of Backward Semilinear Subdiffusion Problems

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