TWO FULLY DISCRETE SCHEMES FOR FRACTIONAL DIFFUSION AND DIFFUSION-WAVE EQUATIONS WITH NONSMOOTH DATA Academic Article uri icon

abstract

  • 2016 Society for Industrial and Applied Mathematics. We consider initial/boundary value problems for the subdiffusion and diffusion-wave 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.

published proceedings

  • SIAM JOURNAL ON SCIENTIFIC COMPUTING

altmetric score

  • 0.75

author list (cited authors)

  • Jin, B., Lazarov, R., & Zhou, Z.

citation count

  • 181

complete list of authors

  • Jin, Bangti||Lazarov, Raytcho||Zhou, Zhi

publication date

  • January 1, 2016 11:11 AM