In this article, we develop and analyze two-grid/multi-level algorithms via mesh refinement in the abstract framework of Brezzi, Rappaz, and Raviart for approximation of branches of nonsingular solutions. Optimal fine grid accuracy of two-grid/multi-level algorithms can be achieved via the proper scaling of relevant meshes. An important aspect of the proposed algorithms is the use of mesh refinement in conjunction with Newton-type methods for system solution in contrast to the usual Newton’s method on a fixed mesh. The pseudostress-velocity formulation of the stationary, incompressible Navier–Stokes equations is considered as an application and the Raviart–Thomas mixed finite element spaces are used for the approximation. Finally, several numerical examples are presented to test the performance of the algorithm and validity of the theory developed.
Bibliographical noteFunding Information:
Dongho Kim was supported by NRF-2018R1D1A1B0705058313. Eun-Jae Park was supported by the National Research Foundation of Korea (NRF) Grant funded by the Ministry of Science and ICT (NRF-2015R1A5A1009350 and NRF-2019R1A2C2090021). Boyoon Seo was supported by NRF-2020R1I1A1A0107036.
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Numerical Analysis
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics