Analysis of two methods based on Galerkin weak form for fractional diffusion-wave: meshless interpolating element free Galerkin (IEFG) and finite element methods. (English) Zbl 1403.65068
Summary: In this paper we apply a finite element scheme and interpolating element free Galerkin technique for the numerical solution of the two-dimensional time fractional diffusion-wave equation on the irregular domains. The time fractional derivative which has been described in the Caputos sense is approximated by a scheme of order \(\mathcal O(\tau^{3-\alpha})\), \(1<\alpha<2\), and the space derivatives are discretized with finite element and interpolating element free Galerkin techniques. We prove the unconditional stability and obtain an error bound for the two new schemes using the energy method. However we would like to emphasize that the main aim of the current paper is to implement the Galerkin finite element method and interpolating element free Galerkin method on complex domains. Also we present error estimate for both schemes proposed for solving the time fractional diffusion-wave equation. Numerical examples demonstrate the theoretical results and the efficiency of the proposed scheme.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
time fractional diffusion-wave equation; finite element method (FEM); (interpolating) element free Galerkin method and (interpolating) moving least squares approximation; energy method; unconditional stability and convergence; irregular domainsSoftware:
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