Two-grid stabilized finite element methods with backtracking for the stationary Navier-Stokes equations

• Published in: Advances in computational mathematics Vol. 50; no. 4
• Main Authors: Han, Jing, Du, Guangzhi
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2024; Springer Nature B.V
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Error analysis; Error correction; Finite element method; Fluid flow; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Navier-Stokes equations; Nonlinear systems; Visualization; Two-grid method; Backtracking technique; Local Gauss integral technique; Stabilized finite element method; 76M10; 65N30; Navier-Stokes equations
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-024-10180-1

Based on local Gauss integral technique and backtracking technique, this paper presents and studies three kinds of two-grid stabilized finite element algorithms for the stationary Navier-Stokes equations. The proposed methods consist of deducing a coarse solution on the nonlinear system, updating the solution on a fine mesh via three different methods, and solving a linear correction problem on the coarse mesh to obtain the final solution. The error estimates are derived for the solution approximated by the proposed algorithms. A series of numerical experiments are illustrated to test the applicability and efficiency of our proposed methods, and support the theoretical analysis results.