Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation

Abstract

In this article, a fully discrete local discontinuous Galerkin (LDG) method with high-order temporal convergence rate is presented and developed to look for the numerical solution of nonlinear time-fractional fourth-order partial differential equation (PDE). In the temporal direction, for approximating the fractional derivative with order α∈(0,1), the weighted and shifted Grünwald difference (WSGD) scheme with second-order convergence rate is introduced and for approximating the integer time derivative, two step backward Euler method with second-order convergence rate is used. For the spatial direction, the LDG method is used. For the numerical theories, the stability is derived and a priori error results are proved. Further, some error results and convergence rates are calculated by numerical procedure to illustrate the effectiveness of proposed method.