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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Multi-level adaptive solutions to boundary-value problems


Author: Achi Brandt
Journal: Math. Comp. 31 (1977), 333-390
MSC: Primary 65N05
MathSciNet review: 0431719
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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

DOI: http://dx.doi.org/10.1090/S0025-5718-1977-0431719-X
PII: S 0025-5718(1977)0431719-X
Article copyright: © Copyright 1977 American Mathematical Society