Unconditional stability and optimal error analysis of mass conservative characteristic mixed FEM for wormhole propagation

Abstract

This paper is concerned with unconditional stability and optimal convergence of mass conservative type method for simulating wormhole propagation in porous media. Specifically, mass conservative characteristic finite element method (FEM) is used for the solute transport equation, the mixed FEM is used for velocity-pressure equation and Galerkin FEM for porosity equation. By error splitting technique, we prove the error of the solution between full discrete system and time discrete system is time-independent, while the numerical solution is bounded without certain time step restriction. Moreover, the optimal L2 error estimates further hold in a general case by elliptic quasi-projection, where the unconditional r+1 order accuracy of the concentration and porosity can be obtained with no loss of accuracy for r order approximation velocity-pressure equation. Numerical experiments are presented to verify the theoretical analysis and the effectiveness of the proposed method.