A local projection stabilization virtual element method for the time-fractional Burgers equation with high Reynolds numbers

Abstract

We propose and analyze a local projection stabilization virtual element method for time-fractional Burgers equation on polygonal meshes, whose solutions display a weak singularity at the initial time. Based on the L1 scheme on a graded mesh in time and virtual element method in space, the stability and existence and uniqueness of the fully discrete scheme are proved; and the priori error estimates in L2 norm is derived with local projection stabilization term. Numerical experiments show that our method is effective for time fractional Burgers equation with high Reynolds number.