A least squares procedure for the wave equation

Author:
Alfred Carasso

Journal:
Math. Comp. **28** (1974), 757-767

MSC:
Primary 65N05

DOI:
https://doi.org/10.1090/S0025-5718-1974-0373310-7

MathSciNet review:
0373310

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Abstract: We develop and analyze a least squares procedure for approximating the homogeneous Dirichlet problem for the wave equation in a bounded domain in . This procedure is based on the pure implicit scheme for time differencing. Surprisingly, it is the normal derivative of *u* rather than *u* itself which must be included in the boundary functional. This normal derivative is an unknown quantity. We show that it may be set equal to zero while retaining the accuracy of the pure implicit scheme. The penalty is that one must use smoother trial functions to obtain this accuracy.

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DOI:
https://doi.org/10.1090/S0025-5718-1974-0373310-7

Article copyright:
© Copyright 1974
American Mathematical Society