Multi-level adaptive solutions to boundary-value problems

Author:
Achi Brandt

Journal:
Math. Comp. **31** (1977), 333-390

MSC:
Primary 65N05

DOI:
https://doi.org/10.1090/S0025-5718-1977-0431719-X

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 operations (40*n* 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 "-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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DOI:
https://doi.org/10.1090/S0025-5718-1977-0431719-X

Article copyright:
© Copyright 1977
American Mathematical Society