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An $$L^\infty$$ estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials. (English) Zbl 0315.65062

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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##### References:
 [1] J. H. BRAMBLE and J. E. OSBORN, Rate of convergence estimates for nonselfadjoint eigenvalue approximations, Math. Comp., 27 (1973), 525-549. Zbl0305.65064 MR366029 · Zbl 0305.65064 [2] J. Jr DOUGLAS, and T. DUPONTGalerkin approximations for the two point boundary problem using continuous piecewise-polynomial spaces, Numer. Math.,, 22 (1974), 99-109. Zbl0331.65051 MR362922 · Zbl 0331.65051 [3] J. Jr DOUGLAS, and T. DUPONT, Superconvergence for Galerkin methods for the two point boundary problem via local projections, Numer. Math., 21 (1973), 270-278. Zbl0281.65046 MR331798 · Zbl 0281.65046 [4] J. Jr. DOUGLAS, T. DUPONT and L. WAHLBIN, Optimal L\infty error estimates for Galerkin approximations to solutions of two point boundary problems, to appear. Zbl0306.65053 · Zbl 0306.65053 [5] J. Jr. DOUGLAS, T. DUPONT and M. F. WHEELER, A quasi-projection approximation applied to Galerkin procedures for parabolic and hyperbolic equations, to appear. [6] J. Jr. DOUGLAS, T. DUPONT and M. F. WHEELER, A Galerkin procedure for approximating the flux on the boundary for elliptic and parabolic boundary value problems, this Journal, 47-59. Zbl0315.65063 MR359357 · Zbl 0315.65063
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