Coupled sound and heat flow and the method of least squares
Author:
Alfred Carasso
Journal:
Math. Comp. 29 (1975), 447463
MSC:
Primary 65M15
MathSciNet review:
0395252
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Abstract: We construct and analyze a leastsquares procedure for approximately solving the initialvalue problem for the linearized equations of coupled sound and heat flow, in a bounded domain in , with homogeneous Dirichlet boundary conditions. The method is based on CrankNicolson time differencing. To approximately solve the resulting system of boundary value problems at each time step, a leastsquares method is devised, using trial functions which need not satisfy the homogeneous boundary conditions. Certain unknown normal derivatives of the solution enter the boundary integrals. By using suitable weights, these unknown derivatives can be set equal to zero without impairing the accuracy of the CrankNicolson scheme. However, one must use smoother trial functions to obtain this accuracy.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197503952524
PII:
S 00255718(1975)03952524
Article copyright:
© Copyright 1975
American Mathematical Society
