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Convergence analysis of a Petrov-Galerkin method for fractional wave problems with nonsmooth data

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arxiv 1901.02799 v2 pith:H24BAEDJ submitted 2019-01-09 math.NA cs.NA

Hao Luo , Binjie Li , Xiaoping Xie This is my paper · ORCID
classification math.NAcs.NA
keywords convergencedatafractionalnonsmoothwaveanalysismethodpetrov-galerkin
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This paper analyzes the convergence of a Petrov-Galerkin method for time fractional wave problems with nonsmooth data. Well-posedness and regularity of the weak solution to the time fractional wave problem are firstly established. Then an optimal convergence analysis with nonsmooth data is derived. Moreover, several numerical experiments are presented to validate the theoretical results.

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  1. Analysis of a time-stepping discontinuous Galerkin method for fractional diffusion-wave equation with nonsmooth data

    math.NA 2019-08 conditional novelty 6.0 of 10

    The time-stepping discontinuous Galerkin method for fractional diffusion-wave problems is shown to achieve nearly optimal O(ln(T/τ)(sqrt(ln(1/h)) h^2 + τ)) accuracy even with nonsmooth data.

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