Local refinement techniques for elliptic problems on cell-centered grids. I. Error analysis
TL;DR: A finite difference technique on rectangular cell-centered grids with local refinement is proposed in order to derive discretizations of second-order elliptic equations of divergence type approximating the so-called balance equa1 1/2 tion.
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Abstract: A finite difference technique on rectangular cell-centered grids with local refinement is proposed in order to derive discretizations of second-order elliptic equations of divergence type approximating the so-called balance equa1 1/2 tion. Error estimates in a discrete H -norm are derived of order h ' for a simple symmetric scheme, and of order h ' for both a nonsymmetric and a more accurate symmetric one, provided that the solution belongs to H +a for a > \\ and a > \\ , respectively.
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References
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TL;DR: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace.
CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
TL;DR: A Lanczos-type method is presented for nonsymmetric sparse linear systems as arising from discretisations of elliptic partial differential equations, based on a polynomial variant of the conjugate gradients algorithm.
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On convergence of block-centered finite differences for elliptic-problems
Alan Weiser,Mary Wheeler Fanett +1 more
TL;DR: In this paper, the authors consider linear, selfadjoint, elliptic problems with Neumann boundary conditions in rectangular domains and demonstrate that with sufficiently smooth data, the discrete $L^2 $-norm errors for tensor product block-centered finite differences in both the approximate solution and its first derivatives are second-order for all nonuniform grids.
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