Asymptotic behaviour of the Galerkin and the finite element collocation methods for a parabolic equation

被引：12

作者：

Onah, SE ^{[1
]}

机构：

[1] Univ Agr, Dept Math, Makurdi, Benue State, Nigeria

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2002年 / 127卷 / 2-3期

关键词：

spline functions; eigenvalues; spectral norms;

D O I：

10.1016/S0096-3003(00)00166-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The asymptotic convergence of the solution of a parabolic equation is proved. The proof is based on two methods namely, the Galerkin method expressed in terms of linear splines and the Finite Element Collocation method expressed by cubic spline basis functions. Both methods are considered in continuous time. The asymptotic rate of convergence for the two methods is found to be of order O(h(2)). (C) 2002 Elsevier Science Inc. All rights reserved.

引用

页码：207 / 213

页数：7

共 50 条

[21] A CONFORMING DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR SECOND-ORDER PARABOLIC EQUATION
Huo, Fuchang
Sun, Yuchen
Wu, Jiageng
Zhang, Liyuan
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2025, 22 (03) : 432 - 458
[22] Weak Galerkin Finite Element Methods for the Biharmonic Equation on Polytopal Meshes
Mu, Lin
Wang, Junping
Ye, Xiu
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2014, 30 (03) : 1003 - 1029
[23] Stability of Galerkin and collocation time domain boundary element methods as applied to the scalar equation wave
Yu, GY
Mansur, WJ
Carrer, JAM
Gong, L
COMPUTERS & STRUCTURES, 2000, 74 (04) : 495 - 506
[24] Asymptotic behaviour of solutions of a degenerate parabolic equation
Kwak, M
Yu, K
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 45 (01) : 109 - 121
[25] Superconvergence of H1-Galerkin mixed finite element methods for parabolic problems
Tripathy, Madhusmita
Sinha, Rajen K.
APPLICABLE ANALYSIS, 2009, 88 (08) : 1213 - 1231
[26] Weak Galerkin Finite Element Methods for Parabolic Interface Problems with Nonhomogeneous Jump Conditions
Deka, Bhupen
Roy, Papri
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2019, 40 (03) : 259 - 279
[27] Weak Galerkin finite element methods for linear parabolic integro-differential equations
Zhu, Ailing
Xu, Tingting
Xu, Qiang
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2016, 32 (05) : 1357 - 1377
[28] Discontinuous Galerkin finite element method for parabolic problems
Kaneko, Hideaki
Bey, Kim S.
Hou, Gene J. W.
APPLIED MATHEMATICS AND COMPUTATION, 2006, 182 (01) : 388 - 402
[29] Flexible Galerkin finite element methods
Adjerid, S
Massey, TC
COMPUTATIONAL FLUID AND SOLID MECHANICS 2003, VOLS 1 AND 2, PROCEEDINGS, 2003, : 1848 - 1850
[30] A domain decomposition Taylor Galerkin finite element approximation of a parabolic singularly perturbed differential equation
Kumar, Sunil
Kumar, B. V. Rathish
APPLIED MATHEMATICS AND COMPUTATION, 2017, 293 : 508 - 522

← 1 2 3 4 5 →