Abstract
By using a special interpolation operator developed by Girault and Raviart (finite element methods for Navier-Stokes Equations, Springer-Verlag, Berlin, 1986), we prove that optimal error bounds can be obtained for a fourth-order elliptic problem and a fourth-order parabolic problem solved by mixed finite element methods on quasi-uniform rectangular meshes. Optimal convergence is proved for all continuous tensor product elements of order k ≥ 1. A numerical example is provided for solving the fourth-order elliptic problem using the bilinear element. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006
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