Document Zbl 0466.65071

A conservative finite element method for one-dimensional Stefan problems with appearing and disappearing phases. (English) Zbl 0466.65071

J. Comput. Phys. 41, 357-388 (1981).

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MSC:

65Z05	Applications to the sciences
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35K05	Heat equation
35R35	Free boundary problems for PDEs
80A17	Thermodynamics of continua

Keywords:

Stefan problem; several phases; front-tracking method; finite elements; moving boundaries; conservation of heat energy; numerical experiments

Citations:

Zbl 0415.65058

Cite Review PDF

Full Text: DOI

References:

[1]	Bonnerot, R.; Jamet, P., J. Comput. Phys., 32, 145-167 (1979) · Zbl 0415.65058
[2]	Cannon, J. R.; Douglas, J.; Denson Hill, C., J. Math. Mech., 17, 21-33 (1967) · Zbl 0154.36501
[3]	Cannon, J. R.; Primicerio, M., SIAM J. Math. Anal., 4, 141-148 (1973) · Zbl 0224.35044
[4]	Ciarlet, P., The Finite Element Method for Elliptic Problems (1978), North-Holland: North-Holland Amsterdam · Zbl 0383.65058
[5]	Douglas, J.; Dupont, T.; Wheeler, M. F., RAIRO, 2, 47-59 (1974) · Zbl 0315.65063
[6]	Furzeland, R. M., A Survey of the Formulation and Solution of Free and Moving Boundary (Stefan) Problems, (Report TR/76 (1977), Brunel University) · Zbl 0468.65063
[7]	Jamet, P., SIAM J. Numer. Anal., 15, 912-928 (1978) · Zbl 0434.65091
[8]	Jamet, P.; Bonnerot, R., J. Comput. Phys., 18, 21-45 (1975) · Zbl 0303.76030
[9]	Nitsche, J. A., (Proceedings, Intensive Seminar on Free Boundary Problems. Proceedings, Intensive Seminar on Free Boundary Problems, Pavia (1979)), in press
[10]	Ockendon, J. R.; Hodgkins, W. R., Moving Boundary Problems in Heat Flow and Diffusion (1975), Clarendon: Clarendon Oxford · Zbl 0295.76064
[11]	Sherman, B., J. Math. Anal. Appl., 33, 449-466 (1971) · Zbl 0203.40901
[12]	Wilson, D. G.; Solomon, A. D.; Boggs, P. T., Moving Boundary Problems (1978), Academic Press: Academic Press New York
[13]	Wilson, D. G.; Solomon, A. D.; Trent, J. S., A Bibliography on Moving Boundary Problems with Key Word Index, (Report ORNL/CSD-44 (1979), Oak Ridge National Laboratory)
[14]	Bonnerot, R.; Jamet, P., J. Numer. Meth. Engrg., 8, 811-820 (1974) · Zbl 0285.65071
[15]	Gautier, B.; Joecklié, R., (Proceedings, Second International Conference on Lasers and Applications. Proceedings, Second International Conference on Lasers and Applications, Orlando, Florida (December 1979))
[16]	Jochum, P., Numer. Math., 34, 411-429 (1980) · Zbl 0411.65058
[17]	Varóglu, E.; Finn, L., J. Comput. Phys., 34, 371-389 (1980) · Zbl 0487.76083

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