Multilevel adaptive solutions to boundaryvalue problems
Author:
Achi Brandt
Journal:
Math. Comp. 31 (1977), 333390
MSC:
Primary 65N05
DOI:
https://doi.org/10.1090/S0025571819770431719X
MathSciNet review:
0431719
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Abstract: The boundaryvalue problem is discretized on several grids (or finiteelement 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 mixedtype (transonic flow) problemsconfirm theoretical predictions. Similar techniques for initialvalue problems are briefly discussed.

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© Copyright 1977
American Mathematical Society