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.
Convergence analysis of a Petrov-Galerkin method for fractional wave problems with nonsmooth data
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abstract
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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Analysis of a time-stepping discontinuous Galerkin method for fractional diffusion-wave equation with nonsmooth data
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.