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TWOPOINT BOUNDARY VALUE PROBLEMS
ELLIPTIC BOUNDARYVALUE PROBLEMS
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Academic Press accuracy alternating direction Anal approximate solution approximation properties assume boundary conditions boundary value problems bounded domain Bramble Chapter Ciarlet coefficients Cohen-Macaulay Cohen-Macaulay ring Comp computational convergence defined Dendy denotes described dimension Dirichlet problem discrete discrete-time Galerkin Dupont error estimates estimates are derived example exists a constant family of class finite difference finite dimensional subspace finite element method following theorem Galerkin approximation Galerkin methods Galerkin procedure H ft heat equation hence Hermite polynomials independent of h integrals interpolation iteration Lemma Let R,m linear m+l m Math Mathematical matrix nonlinear norm obtain optimal L estimates parabolic problems Partial Differential Equations partition piecewise polynomials polynomials of degree proof quadrature R-module regular local ring ring R,m satisfies shown SIAM solving space variable splines subspace subspace of H sufficiently smooth superconvergence t e 0,T techniques Thomee triangle inequality Wahlbin Zlamal