A hybrid high-order method for Sobolev equation with convection-dominated term

Abstract

We consider a new hybrid high-order method for the Sobolev equation with convection-dominated term. We adopt the Pk polynomials to approximate the primary unknown on mesh elements and faces where k is a given positive integer. The stability and high accuracy are obtained by using reconstruction to formulate the gradient term and convective term and by adding a suitable stabilization term. We analyze the semi-discrete formulation of the hybrid high-order method and use Crank-Nicolson difference in time to get the corresponding fully-discrete scheme. We prove stability and convergence of the approximate solution in energy norm. The energy errors hold irrespective of the reciprocal of dispersion, diffusion and reaction coefficients. Numerical results underline the efficiency of the proposed methods and our analytical findings.