Local refinement techniques for elliptic problems on cell-centered grids. I. Error analysis
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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.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.read more
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References
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Book
Finite Element Solution of Boundary Value Problems: Theory and Computation
Owe Axelsson,V.A. Barker +1 more
TL;DR: Finite Element Solution of Boundary Value Problems: Theory and Computation as mentioned in this paper provides a thorough, balanced introduction to both the theoretical and the computational aspects of the finite element method for solving boundary value problems for partial differential equations.
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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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Bounds for a class of linear functionals with applications to Hermite interpolation
James H. Bramble,Stephen Hilbert +1 more
TL;DR: In this article, a general estimation theorem is given for a class of linear functionals on Sobolev spaces, which are those which annihilate certain classes of polynomials, and an interpolation scheme of Hermite type is defined in N-dimensions.
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