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The coupling of hyperbolic and elliptic boundary value problems with variable coefficients

✍ Scribed by Cristian A. Coclici; Gheorghe Moroşanu; Wolfgang L. Wendland

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
298 KB
Volume
23
Category
Article
ISSN
0170-4214

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✦ Synopsis

We consider a one-dimensional coupled problem for elliptic second-order ODEs with natural transmission conditions. In one subinterval, the coe$cient '0 of the second derivative tends to zero. Then the equation becomes there hyperbolic and the natural transmission conditions are not ful"lled anymore. The solution of the degenerate coupled problem with a #ux transmission condition is corrected by an internal boundary layer term taking into account the viscosity . By using singular perturbation techniques, we show that the remainders in our "rst-order asymptotic expansion converge to zero uniformly. Our analysis provides an a posteriori correction procedure for the numerical treatment of exterior viscous compressible #ow problems with coupled Navier}Stokes/Euler models.

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