Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8959546 | Journal of Mathematical Analysis and Applications | 2018 | 17 Pages |
Abstract
In this paper, we present a scheme for solving two-dimensional miscible displacement problems using Eulerian-Lagrangian localized adjoint methods and mixed finite element methods. Since only the velocity and not the pressure appears explicitly in the concentration equation, an Eulerian-Lagrangian localized adjoint method is used to solve the concentration equation and a mixed finite element method is used for the pressure equation. To linearize and decouple the mixed-method equations, we use a two-grid algorithm based on the Newton iteration method for this fully discrete problems. First, we solve the original nonlinear equations on the coarse grid, then, we solve the linearized problem on the fine grid using Newton iteration once. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h1/2) in this paper.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yang Wang, Yanping Chen,