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The penalty method for grid matching in mixed finite element methods. (English. Russian original) Zbl 1178.65141

Russ. Math. 53, No. 3, 29-44 (2009); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 3, 37-54 (2009).
The finite element method of Hermann-Hellan-Johnson [F. Brezzi and P. A. Raviart, Mixed finite element methods for 4th order elliptic equations. Topics in numerical analysis III, Proc. R. Irish Acad. Conf., Dublin 1976, 33–56 (1977; Zbl 0434.65085); R. S. Falk and J. E. Osborn, RAIRO, Anal. Numér. 14, 249–277 (1980; Zbl 0467.65062)] for the biharmonic equation is considered for non-matching grids. Matching conditions are replaced by penalty terms. The convergence rate is less than that of the mixed finite element method on matching grids with any choice of penalty parameters. This is in contrast to results by the authors for other finite element methods.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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References:

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