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Single Step Fully Discrete Approximations
6 other sections not shown
approximately solve assume Baker and Bramble boundary value problem bounded operator Bramble and Sammon Chapter completes the proof conjugate gradient algorithms cp e H defined dependent coefficients eigenfunctions eigenvalues Em+1 error equation error estimates follows fully discrete approximation fully discrete equation fully discrete scheme functions gives Hilbert space I+aB2 imply induction hypothesis initial guess inner product invertible iterative methods Jth time derivative lemma Lemma 3.1 linear Lions and Magenes matrix methods for approximately nonnegative integer norm number of iterations ordinary differential equations orthogonal projection partial differential equations positive definite positive integer preconditioned conjugate gradient preconditioner preconditioning operator proof of Theorem properties Sammon 20 satisfies second order hyperbolic self-adjoint self-adjoint operator SEMIDISCRETE AND SINGLE seminorm Sh x Sh single step fully single step methods special choice special initial data step fully discrete subspaces t e 0,T Theorem 5.1 triangle inequality