Fractional Crank–Nicolson–Galerkin finite element scheme for the time‐fractional nonlinear diffusion equation

• Published in: Numerical methods for partial differential equations Vol. 35; no. 6; pp. 2056 - 2075
• Main Authors: Kumar, Dileep, Chaudhary, Sudhakar, Srinivas Kumar, V.V.K.
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.11.2019; Wiley Subscription Services, Inc
• Subjects: Convolution; discrete fractional Gronwall type inequality; error estimates; Finite element method; fractional Crank–Nicolson method; Galerkin method; Newton methods; Quadratures; time‐fractional diffusion equation

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 t...