Finite element methods for parabolic equations
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- by Miloš Zlámal PDF
- Math. Comp. 28 (1974), 393-404 Request permission
Abstract:
The initial-boundary value problem for a linear parabolic equation with the Dirichlet boundary condition is solved approximately by applying the finite element discretization in the space dimension and three types of finite-difference discretizations in time: the backward, the Crank-Nicolson and the Calahan discretization. New error bounds are derived.References
- James H. Bramble and Vidar Thomée, Semidiscrete least-squares methods for a parabolic boundary value problem, Math. Comp. 26 (1972), 633–648. MR 349038, DOI 10.1090/S0025-5718-1972-0349038-4
- James H. Bramble and Vidar Thomée, Discrete time Galerkin methods for a parabolic boundary value problem, Ann. Mat. Pura Appl. (4) 101 (1974), 115–152. MR 388805, DOI 10.1007/BF02417101
- Jim Douglas Jr. and Todd Dupont, Galerkin methods for parabolic equations, SIAM J. Numer. Anal. 7 (1970), 575–626. MR 277126, DOI 10.1137/0707048
- C. William Gear, Numerical initial value problems in ordinary differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0315898
- Ivan Hlaváček, On a semi-variational method for parabolic equations. I, Apl. Mat. 17 (1972), 327–351 (English, with Czech summary). MR 314285
- O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural′ceva, Lineĭ nye i kvazilineĭ nye uravneniya parabolicheskogo tipa, Izdat. “Nauka”, Moscow, 1967 (Russian). MR 0241821 W. Visser, A Finite Element Method For the Determination of Non-Stationary Temperature Distribution and Thermal Deformations, Proc. Conf. Matrix Meth. Struct. Mech., Air Force Inst. of Techn., Wright-Patterson A. F. Base, Ohio, 1965. E. L. Wilson & R. E. Nickell, "Application of finite element method to heat conduction analysis," Nuclear Eng. Design, v. 4, 1966, pp. 276-286. M. Zlámal, "Some recent advances in the mathematics of finite elements," in The Mathematics of Finite Elements and Applications, edited by J. R. Whiteman, Academic Press, London, 1972, pp. 59-81. M. Zlámal, "The finite element method in domains with curved boundaries," Int. J. Numer. Meth. Eng., v. 5, 1973, pp. 367-373.
- Miloš Zlámal, Curved elements in the finite element method. I, SIAM J. Numer. Anal. 10 (1973), 229–240. MR 395263, DOI 10.1137/0710022
- Miloš Zlámal, Curved elements in the finite element method. II, SIAM J. Numer. Anal. 11 (1974), 347–362. MR 343660, DOI 10.1137/0711031
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 393-404
- MSC: Primary 65N35
- DOI: https://doi.org/10.1090/S0025-5718-1974-0388813-9
- MathSciNet review: 0388813