Galerkin finite element approximation of symmetric space-fractional partial differential equations |
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Authors: | H Zhang V Anh |
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Institution: | a School of Mathematical and Computer Sciences, Fuzhou University, Fuzhou 350108, China b School of Mathematical Sciences, Queensland University of Technology, Qld. 4001, Australia |
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Abstract: | In this paper, symmetric space-fractional partial differential equations (SSFPDE) with the Riesz fractional operator are considered. The SSFPDE is obtained from the standard advection-dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order 2β ∈ (0, 1) and 2α ∈ (1, 2], respectively. We prove that the variational solution of the SSFPDE exists and is unique. Using the Galerkin finite element method and a backward difference technique, a fully discrete approximating system is obtained, which has a unique solution according to the Lax-Milgram theorem. The stability and convergence of the fully discrete schemes are derived. Finally, some numerical experiments are given to confirm our theoretical analysis. |
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Keywords: | Galerkin finite element approximation Space-fractional partial differential equations Stability Convergence |
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