Error Estimates of a Pressure-Stabilized Characteristics Finite Element Scheme for the Oseen Equations
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Error estimates with the optimal convergence order are proved for a pressure-stabilized characteristics finite element scheme for the Oseen equations. The scheme is a combination of Lagrange–Galerkin finite element method and Brezzi–Pitkäranta’s stabilization method. The scheme maintains the advantages of both methods; (i) It is robust for convection-dominated problems and the system of linear equations to be solved is symmetric. (ii) Since the P1 finite element is employed for both velocity and pressure, the number of degrees of freedom is much smaller than that of other typical elements for the equations, e.g., P2/P1. Therefore, the scheme is efficient especially for three-dimensional problems. The theoretical convergence order is recognized by two- and three-dimensional numerical results.
KeywordsError estimates The finite element method The method of characteristics Pressure-stabilization The Oseen equations
Mathematics Subject Classification65M12 65M60 65M25 76D07
The authors are thankful to anonymous referees for their valuable comments. This work was supported by JSPS (the Japan Society for the Promotion of Science) under the Japanese-German Graduate Externship (Mathematical Fluid Dynamics) and by Waseda University under Project research, Spectral analysis and its application to the stability theory of the Navier–Stokes equations of Research Institute for Science and Engineering. The authors are indebted to JSPS also for Grant-in-Aid for Young Scientists (B), No. 26800091 to the first author and for Grants-in-Aid for Scientific Research (C), No. 25400212 and (S), No. 24224004 to the second author.
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