Symmetric fractional order reduction method with L1 scheme on graded mesh for time fractional nonlocal diffusion-wave equation of Kirchhoff type
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In this article, we propose a linearized fully-discrete scheme for solving a time fractional nonlocal diffusion-wave equation of Kirchhoff type. The scheme is established by using the finite element method in space and the L1 scheme in time. We derive the α-robust a priori bound and a priori error estimate for the fully-discrete solution in L^∞(H^1_0(Ω)) norm, where α∈ (1,2) is the order of time fractional derivative. Finally, we perform some numerical experiments to verify the theoretical results.
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