An ADI Finite Volume Element Method for a Viscous Wave Equation with Variable Coefficients

Based on rectangular partition and bilinear interpolation, we construct an alternating-direction implicit (ADI) finite volume element method, which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients. This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes. Optimal error estimate in L2 norm is obtained for the schemes. Compared with the finite volume element method of the same convergence order, our method is more effective in terms of running time with the increasing of the computing scale. Numerical experiments are presented to show the efficiency of our method and numerical results are provided to support our theoretical analysis.