Finite element methods for parabolic equations

Author:
Miloš Zlámal

Journal:
Math. Comp. **28** (1974), 393-404

MSC:
Primary 65N35

DOI:
https://doi.org/10.1090/S0025-5718-1974-0388813-9

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.

- 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 https://doi.org/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 https://doi.org/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 https://doi.org/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, - Miloš Zlámal,
*Curved elements in the finite element method. I*, SIAM J. Numer. Anal.**10**(1973), 229–240. MR**395263**, DOI https://doi.org/10.1137/0710022 - Miloš Zlámal,
*Curved elements in the finite element method. II*, SIAM J. Numer. Anal.**11**(1974), 347–362. MR**343660**, DOI https://doi.org/10.1137/0711031

*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.

Retrieve articles in *Mathematics of Computation*
with MSC:
65N35

Retrieve articles in all journals with MSC: 65N35

Additional Information

Article copyright:
© Copyright 1974
American Mathematical Society