Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 38, Issue 1, Pages A146-A170Publisher
SIAM PUBLICATIONS
DOI: 10.1137/140979563
Keywords
fractional diffusion; diffusion wave; finite element method; convolution quadrature; error estimate
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Funding
- UK Engineering and Physical Sciences Research Council [EP/M025160/1]
- Engineering and Physical Sciences Research Council [EP/M025160/1] Funding Source: researchfish
- EPSRC [EP/M025160/1] Funding Source: UKRI
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We consider initial/boundary value problems for the subdiffusion and diffusion-ave equations involving a Caputo fractional derivative in time. We develop two fully discrete schemes based on the piecewise linear Galerkin finite element method in space and convolution quadrature in time with the generating function given by the backward Euler method/second-order backward difference method, and establish error estimates optimal with respect to the regularity of problem data. These two schemes are first-and second-order accurate in time for both smooth and nonsmooth data. Extensive numerical experiments for two-dimensional problems confirm the convergence analysis and robustness of the schemes with respect to data regularity.
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