Finite difference/finite element method for tempered time fractional advection-dispersion equation with fast evaluation of Caputo derivative. (English) Zbl 1453.65311
Summary: In this paper, a class of fractional advection-dispersion equations with Caputo tempered fractional derivative are considered numerically. An efficient algorithm for the evaluation of Caputo tempered fractional derivative is proposed to sharply reduce the computational work and storage, and this is of great significance for large-scale problems. Based on the nonsmooth regularity assumptions, a semi-discrete form is obtained by finite difference method in time, and its stability and convergence are investigated. Then by finite element method, we derive the corresponding fully discrete scheme and discuss its convergence. At last, some numerical examples, based on different domains, are presented to demonstrate effectiveness of numerical schemes and confirm the theoretical analysis.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
time fractional advection-dispersion equation; finite difference method; finite element method; stability analysis; convergence analysis; fast evaluationReferences:
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