Finite element multistep discretizations of parabolic boundary value problems

Zlámal, Miloš

doi:10.1090/S0025-5718-1975-0371105-2

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Browser Compatibility Info Help
ISSN 1088-6842(online) ISSN 0025-5718(print)

Finite element multistep discretizations of parabolic boundary value problems

Author: Miloš Zlámal
Journal: Math. Comp. 29 (1975), 350-359
MSC: Primary 65N30
MathSciNet review: 0371105
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The initial-boundary value problem for a linear parabolic equation in an infinite cylinder under the Dirichlet boundary condition is solved by applying the finite element discretization in the space dimension and ${A_0}$ -stable multistep discretizations in time. No restriction on the ratio of the time and space increments is imposed. The methods are analyzed and bounds for the discretization error in the ${L_2}$ -norm are given.

[1] 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)
[2] P. G. Ciarlet and P.-A. Raviart, Interpolation theory over curved elements, with applications to finite element methods, Comput. Methods Appl. Mech. Engrg. 1 (1972), 217–249. MR 0375801 (51 #11991)
[3] Colin W. Cryer, A new class of highly-stable methods: 𝐴₀-stable methods, Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 153–159. MR 0323111 (48 #1469)
[4] Colin W. Cryer, On the instability of high order backward-difference multistep methods, Nordisk Tidskr. Informations behandling (BIT) 12 (1972), 17–25. MR 0311112 (46 #10208)
[5] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons Inc., New York, 1962. MR 0135729 (24 #B1772)
[6] O. A. LADYŽENSKAJA, V. A. SOLONNIKOV & N. N. URAL'CEVA, Linear and Quasi-Linear Equations of Parabolic Type, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, R. I., 1968. MR 39 #3159b.
[7] J. D. Lambert, Computational methods in ordinary differential equations, John Wiley & Sons, London-New York-Sydney, 1973. Introductory Mathematics for Scientists and Engineers. MR 0423815 (54 #11789)
[8] O. C. Zienkiewicz, The finite element method in engineering science, McGraw-Hill, London, 1971. The second, expanded and revised, edition of The finite element method in structural and continuum mechanics. MR 0315970 (47 #4518)
[9] Miloš Zlámal, Finite element methods for parabolic equations, Math. Comp. 28 (1974), 393–404. MR 0388813 (52 #9647), http://dx.doi.org/10.1090/S0025-5718-1974-0388813-9
[10] Miloš Zlámal, Curved elements in the finite element method. I, SIAM J. Numer. Anal. 10 (1973), 229–240. MR 0395263 (52 #16060)
[11] Miloš Zlámal, Curved elements in the finite element method. II, SIAM J. Numer. Anal. 11 (1974), 347–362. MR 0343660 (49 #8400)

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|