|
Finite element methods for parabolic equations
Author:
Miloš Zlámal
Journal:
Math. Comp. 28 (1974), 393-404
MSC:
Primary 65N35
MathSciNet review:
0388813
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
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.
- [1]
James
H. Bramble and Vidar
Thomée, Semidiscrete least-squares methods for
a parabolic boundary value problem, Math.
Comp. 26 (1972),
633–648. MR 0349038
(50 #1532), http://dx.doi.org/10.1090/S0025-5718-1972-0349038-4
- [2]
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 0388805
(52 #9639)
- [3]
Jim
Douglas Jr. and Todd
Dupont, Galerkin methods for parabolic equations, SIAM J.
Numer. Anal. 7 (1970), 575–626. MR 0277126
(43 #2863)
- [4]
C.
William Gear, Numerical initial value problems in ordinary
differential equations, Prentice-Hall Inc., Englewood Cliffs, N.J.,
1971. MR
0315898 (47 #4447)
- [5]
Ivan
Hlaváček, On a semi-variational method for parabolic
equations. I, Apl. Mat. 17 (1972), 327–351
(English, with Czech summary). MR 0314285
(47 #2837)
- [6]
O.
A. Ladyženskaja, V.
A. Solonnikov, and N.
N. Ural′ceva, Linear and quasilinear equations of parabolic
type, Translated from the Russian by S. Smith. Translations of
Mathematical Monographs, Vol. 23, American Mathematical Society,
Providence, R.I., 1968 (Russian). MR 0241822
(39 #3159b)
- [7]
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.
- [8]
E. L. Wilson & R. E. Nickell, "Application of finite element method to heat conduction analysis," Nuclear Eng. Design, v. 4, 1966, pp. 276-286.
- [9]
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.
- [10]
M. Zlámal, "The finite element method in domains with curved boundaries," Int. J. Numer. Meth. Eng., v. 5, 1973, pp. 367-373.
- [11]
Miloš
Zlámal, Curved elements in the finite element method.
I, SIAM J. Numer. Anal. 10 (1973), 229–240. MR 0395263
(52 #16060)
- [12]
Miloš
Zlámal, Curved elements in the finite element method.
II, SIAM J. Numer. Anal. 11 (1974), 347–362. MR 0343660
(49 #8400)
- [1]
- J. H. Bramble & V. Thomée, "Semidiscrete-least squares methods for a parabolic boundary value problem," Math. Comp., v. 26, 1972, pp. 633-648. MR 0349038 (50:1532)
- [2]
- J. H. Bramble & V. Thomée, "Discrete time Galerkin methods for a parabolic boundary value problem," Ann. Mat. Pura Appl. (To appear.) MR 0388805 (52:9639)
- [3]
- J. Douglas, Jr. & T. Dupont, "Galerkin methods for parabolic equations," SIAM J. Numer. Anal., v. 7, 1970, pp. 575-626. MR 43 #2863. MR 0277126 (43:2863)
- [4]
- C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N.J., 1971. MR 0315898 (47:4447)
- [5]
- J. Hlaváček, "On a semi-variational method for parabolic equations. I, II," Apl. Mat., v. 17, 1972, pp. 327-351; ibid., v. 18, 1973, pp. 43-64. MR 0314285 (47:2837)
- [6]
- O. A. Ladyženskaja, V. A. Solonnikov & N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, "Nauka", Moscow, 1967; English transl., Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, R.I., 1968. MR 39 #3159a,b. MR 0241822 (39:3159b)
- [7]
- 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.
- [8]
- E. L. Wilson & R. E. Nickell, "Application of finite element method to heat conduction analysis," Nuclear Eng. Design, v. 4, 1966, pp. 276-286.
- [9]
- 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.
- [10]
- M. Zlámal, "The finite element method in domains with curved boundaries," Int. J. Numer. Meth. Eng., v. 5, 1973, pp. 367-373.
- [11]
- M. Zlámal, "Curved elements in the finite element method. I," SIAM J. Numer. Anal., v. 10, 1973, pp. 229-240. MR 0395263 (52:16060)
- [12]
- M. Zlámal, "Curved elements in the finite element method. II," SIAM J. Numer. Anal., v. 11, 1974, pp. 347-362. MR 0343660 (49:8400)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
65N35
Retrieve articles in all journals
with MSC:
65N35
Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1974-0388813-9
PII:
S 0025-5718(1974)0388813-9
Article copyright:
© Copyright 1974 American Mathematical Society
|
