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arXiv · 1811.08485

Fractional Crank-Nicolson-Galerkin Finite Element Scheme for the Time-Fractional Nonlinear Diffusion Equation

Dileep Kumar·Sudhakar Chaudhary·V. V. K Srinivas Kumar
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Abstract

This article presents a finite element scheme with Newton's method for solving the time-fractional nonlinear diffusion equation. For time discretization, we use the fractional Crank-Nicolson scheme based on backward Euler convolution quadrature. We discuss the existence-uniqueness results for the fully-discrete problem. Discrete fractional Gronwall type inequality for the backward Euler convolution quadrature which is used to approximate the Riemann-Liouville fractional derivative is established by using the idea of D.Li et al. given in [11]. A priori error estimate for the fully-discrete problem in $L^2(\Omega)$ norm is derived. Numerical results based on finite element scheme are provided to validate the theoretical estimates.

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Dileep Kumar, Sudhakar Chaudhary, V. V. K Srinivas Kumar. 2018-11-20. Fractional Crank-Nicolson-Galerkin Finite Element Scheme for the Time-Fractional Nonlinear Diffusion Equation. https://arxiv.org/abs/1811.08485

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