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The Postprocessed Mixed Finite-Element Method for the Navier–Stokes Equations: Refined Error Bounds

 

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Opened Access The Postprocessed Mixed Finite-Element Method for the Navier–Stokes Equations: Refined Error Bounds
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Author: Frutos, Javier de
García Archilla, Juan Bosco
Novo, Julia
Department: Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
Date: 2007
Published in: SIAM Journal on Numerical Analysis, 46 (1), 201-230.
Document type: Article
Abstract: A postprocessing technique for mixed finite-element methods for the incompressible Navier–Stokes equations is analyzed. The postprocess, which amounts to solving a (linear) Stokes problem, is shown to increase the order of convergence of the method to which it is applied by one unit (times the logarithm of the mesh diameter). In proving the error bounds, some superconvergence results are also obtained. Contrary to previous analysis of the postprocessing technique, in the present paper we take into account the loss of regularity suffered by the solutions of the Navier–Stokes equations at the initial time in the absence of nonlocal compatibility conditions of the data.
Cite: Frutos, J.d., García Archilla, J.B. y Novo, J. (2007). The Postprocessed Mixed Finite-Element Method for the Navier–Stokes Equations: Refined Error Bounds. SIAM Journal on Numerical Analysis, 46 (1), 201-230.
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URI: http://hdl.handle.net/11441/57755

DOI: 10.1137/06064458

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