Finite element approximation of the discrete first-order system least squares for elliptic problems
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Abstract
In [Z. Cai and B. C. Shin, SIAM J. Numer. Anal. 40(2002), 307{318], we developed the discrete ¯rst-order system least squares method for the second-order elliptic boundary value prob-lem by directly approximating H(div) \ H(curl)-type space based on the Helmholtz decomposition. Under general assumptions, error estimates were established in the L2 and H1 norms for the vector and scalar variables, respectively. Such error estimates are opti-mal with respect to the required regularity of the solution. In this paper, we study solution methods for solving the system of linear equations arising from the discretization of variational formulation which possesses discrete biharmonic term and focus on numerical results including the performances of multigrid preconditioners and the ¯nite element accuracy.
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