Two-grid method for compressible miscible displacement problem by mixed finite element methods and expanded mixed finite element method of characteristics

• Published in: Numerical algorithms Vol. 89; no. 2; pp. 611 - 636
• Main Author: Hu, Hanzhang
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2022; Springer Nature B.V
• Subjects: Algebra; Algorithms; Approximation; Compressibility; Computer Science; Contamination; Finite element analysis; Finite element method; Grid method; Iterative methods; Mathematical analysis; Method of characteristics; Miscibility; Nonlinear equations; Numeric Computing; Numerical Analysis; Oil recovery; Original Paper; Porous media; Theory of Computation; Velocity; Characteristic expanded mixed finite element method; Mixed finite element method; Two-grid method; Compressible miscible displacement
• ISSN: 1017-1398; 1572-9265
• DOI: 10.1007/s11075-021-01127-4

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium by employing a mixed finite element method (MFEM) for the pressure equation and expanded mixed finite element method with characteristics (CEMFEM) for the concentration equation. The key point is to use a two-grid scheme to linearize the nonlinear term in the coupling equations. The main procedure of the algorithm is to solve small scaled nonlinear equations on the coarse grid and to deal with a linearized system on the fine space using the Newton iteration with the coarse grid solution. Then, it is shown that a two-grid algorithm achieves optimal approximation as long as the mesh sizes satisfy H = O ( h 1 2 ) . Finally, numerical experiments confirmed the numerical analysis of two-grid algorithm.