UNCONDITIONAL CONVERGENCE AND OPTIMAL ERROR ESTIMATES OF A GALERKIN-MIXED FEM FOR INCOMPRESSIBLE MISCIBLE FLOW IN POROUS MEDIA

作者：Li, Buyang^*; Sun, Weiwei

来源：SIAM Journal on Numerical Analysis, 2013, 51(4): 1959-1977.

DOI：10.1137/120871821

• unconditional stability
• optimal error estimate
• Galerkin-mixed FEM
• incompressible miscible flow

In this paper, we study the unconditional convergence and error estimates of a Galerkin-mixed FEM with the linearized semi-implicit Euler scheme for the equations of incompressible miscible flow in porous media. We prove that the optimal L-2 error estimates hold without any time-step (convergence) conditions, while all previous works require certain time-step restrictions. Our theoretical results provide a new understanding on commonly used linearized schemes. The proof is based on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element discretization of corresponding time-discrete PDEs. The approach used in this paper can be applied to more general nonlinear parabolic systems and many other linearized (semi)-implicit time discretizations.

• 出版日期2013
• 单位南京大学