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The moving finite element method: Applications to general partial differential equations with multiple large gradients. (English) Zbl 0482.65061

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65Y99 Computer aspects of numerical algorithms
35L60 First-order nonlinear hyperbolic equations
35Q99 Partial differential equations of mathematical physics and other areas of application
76L05 Shock waves and blast waves in fluid mechanics
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References:
[1] {\scK. Miller and R. Miller}, SIAM J. Numer. Anal., in press.
[2] {\scK. Miller}, SIAM J. Numer. Anal., in press.
[3] Gear, C.W., Comm. assoc. comput. Mach., 14, 176-179, (1971)
[4] Gelinas, R.J., J. comput. phys., 9, No. 2, 222, (1972)
[5] Hindmarsh, A.C.; Byrne, G.D., EPISODE: an effective package for the integration of systems of ordinary differential equations, Lawrence livermore laboratory report UCID-30112, (April 1977), Rev. 1, Computer Documentation
[6] McCormack, R.; Paullay, A.J., Computers and fluids, 2, 339-361, (1974)
[7] Oran, E.S.; Young, T.; Boris, J., (), 43
[8] Oran, E.S.; Boris, J.P.; Young, T.; Flanigan, M.; Burks, T.; Picone, M., Detonations in hydrogen-air and methane-air mixtures, Naval research laboratory preprint, (1979)
[9] Dwyer, H.A.; Kee, R.J.; Sanders, B.R., ()
[10] Oliger, J., (), and subsequent private communications
[11] Oden, J.T., Finite elements of nonlinear continua, (1972), McGraw-Hill New York · Zbl 0235.73038
[12] Strang, G.; Fix, G.J., An analysis of the finite element method, (1973), Prentice-Hall Englewood Cliffs, N.J · Zbl 0278.65116
[13] Doss, S.K.; Miller, K., Moving finite element solution of the vorticity equations, (1974), [See also References 1 and 2 for a brief summary of these results.]
[14] {\scM. J. Djomehri}, “Moving Finite Element Solution of Systems of Partial Differential Equations in 1-Dimension,” Ph.D. Thesis, University of California, Berkeley. · Zbl 0666.76120
[15] Boris, J.P.; Book, D.L.; Boris; Boris, J. comput. phys., J. comput. phys., J. comput. phys., 20, 397, (1976), See also
[16] Byrne, G.C., ()
[17] Concus, P.; Proskurowski, W., Numerical solution of a nonlinear hyperbolic equation by the random choice method, Lawrence Berkeley laboratory report LBL-6487, (December 1977), Rev.
[18] Dwyer, H.A.; Sanders, B.R., Numerical modeling of unsteady flame propagation, Sandia livermore laboratories report SAND 77-8275, (February 1978)
[19] Otey, G.R.; Dwyer, H.A., A numerical study of the interaction of fast chemistry and diffusion, Sandia livermore laboratories report SAND 78-8686, (April 1979)
[20] {\scR. Alexander, P. Manselli, and K. Miller}, to appear.
[21] Alexander, R.; Manselli, P.; Miller, K., Moving finite elements for the Stefan problem in two dimensions, () · Zbl 0493.65068
[22] Sod, G., J. comput. phys., 27, 1-31, (1978)
[23] Hindmarsh, A.C., Preliminary documentation of GEARIB: solution of implicit systems of ODE’s with banded Jacobian, Lawrence livermore laboratory report UCID-30130, (February 1976), Computer Documentation
[24] Hindmarsh, A.C., Solution of block-tridiagonal systems of linear algebraic equations, Lawrence livermore laboratory report UCID-30150, (February 1977), Computer Documentation
[25] Gelinas, R.J.; Hall, D.K.; Nelson, R.G., Nature, 266, No. 559, 229, (1977)
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