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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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


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:
  • MathSciNet review: 0431719