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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Multi-level adaptive solutions to boundary-value problems
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Math. Comp. 31 (1977), 333-390 Request permission

Abstract:

The boundary-value problem is discretized on several grids (or finite-element spaces) of widely different mesh sizes. Interactions between these levels enable us (i) to solve the possibly nonlinear system of n discrete equations in $O(n)$ operations (40n additions and shifts for Poisson problems); (ii) to conveniently adapt the discretization (the local mesh size, local order of approximation, etc.) to the evolving solution in a nearly optimal way, obtaining "$\infty$-order" approximations and low n, even when singularities are present. General theoretical analysis of the numerical process. Numerical experiments with linear and nonlinear, elliptic and mixed-type (transonic flow) problems-confirm theoretical predictions. Similar techniques for initial-value problems are briefly discussed.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Math. Comp. 31 (1977), 333-390
  • MSC: Primary 65N05
  • DOI: https://doi.org/10.1090/S0025-5718-1977-0431719-X
  • MathSciNet review: 0431719