Title: FVMs for the Nonstationary Navier–Stokes Equations
Abstract: In this chapter, we mainly discuss the stabilized lower order finite volumeLower order finite volume methodsFinite Volume Method (FVM) for the nonstationary Navier–Stokes equationsNavier–Stokes equations. Under the same regularity assumption on the exact solution for the corresponding stabilized finite element methodsStabilized finite element methods, the stabilized finite volume methodsFinite Volume Method (FVM) provide approximate solutions with the same optimal convergence rates for $$u_h$$ in the $$H^1$$ norm and $$p_h$$ in the $$L^2$$ norm. Furthermore, under a slightly different regularity assumption on the source term, the stabilized finite volume methodsStabilized finite volume methods can also reach the optimal convergence rate for $$u_h$$ in the $$L^2$$ norm.
Publication Year: 2022
Publication Date: 2022-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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