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A finite element method for time fractional partial differential equations. (English) Zbl 1273.65142

Summary: We consider the finite element method for time fractional partial differential equations. The existence and uniqueness of the solutions are proved by using the Lax-Milgram Lemma. A time stepping method is introduced based on a quadrature formula approach. The fully discrete scheme is considered by using a finite element method and optimal convergence error estimates are obtained. The numerical examples at the end of the paper show that the experimental results are consistent with our theoretical results.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin 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
65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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References:

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