Longtime Convergence of Numerical Approximations for Semilinear Parabolic Equations (Ⅰ)

Longtime Convergence of Numerical Approximations for Semilinear Parabolic Equations (Ⅰ)

在线阅读下载PDF

导出

摘要 The numerical approximations of the dynamical systems governed by semilinear parabolic equations are considered. An abstract framework for long time error estimates is established. When applied to reaction diffusion equation, Navier Stokes equations and Chan Hilliard equation, approximated by Galerkin and nonlinear Galerkin methods in space and by Runge Kutta method in time, our framework yields error estimates uniform in time. The numerical approximations of the dynamical systems governed by semilinear parabolic equations are considered. An abstract framework for long time error estimates is established. When applied to reaction diffusion equation, Navier Stokes equations and Chan Hilliard equation, approximated by Galerkin and nonlinear Galerkin methods in space and by Runge Kutta method in time, our framework yields error estimates uniform in time.

作者武海军李荣华

出处《Northeastern Mathematical Journal》 CSCD 2000年第1期99-126,共28页 东北数学（英文版）

关键词 semilinear parabolic equation Runge Kutta method long time error estimate semilinear parabolic equation Runge Kutta method long time error estimate

分类号 O241.82 [理学—计算数学]

引文网络
相关文献

参考文献21

1[1]Lubich, C. And Ostermann, A., Runge-Kutta Approximation of quasi-linear parabolic equations, Math. Comp., 64(1995), 601－627.
2[2]Heywood, J.G. And Rannacher, R., Finite element approximation of the nonstationary Navier Stokes problem, Part Ⅰ: Regularity of solutions and second-order error estimates for spatial discretization, SIAM J. Numer. Anal., 19(1982), 275－311.
3[3]Heywood, J.G. And Rannaeher, R., Finite element approximation of the nonstationary Navier Stokes problem, Part Ⅲ: Smoothing property and higher order estimates for spatial discretization, SIAM J. Numer. Anal., 25(1988), 489－512.
4[4]Devulder, C. Marion, M. And Titi, E., On the rate of convergence of nonlinear Galerkin methods, Math. Comp., 60(1993), 495－514.
5[5]Johnson, C., Larsson, S., Thomee, V. And Wahlbin, L., Error estimates for spatically discrete approximation of semilinear parabolic equations with nonsmooth date, Math. Comp., 49(1987), 331－357.
6[6]Dekker, K. And Verwer, J.G., Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations. North-Holland, Amsterdam, 1984.
7[7]Larsson, S., The long-time behavior of finite-element approximation of solutions to semilinear parabolic problems, SIAM J, Numer. Anal., 26(1989), 348－365.
8[8]Carr, J. And Pego, R.L., Metastable patterns in solutions of ut=ε2uxx-f(u). Comm. Pure. Appl. Math., 42(1989), 523－576.
9[9]Foias, C. And Temam, R., Structure of the set of stationary solutions of the Navier-Stokes equations., Comm. Pure Appl. Math., 30(1977), 146－164.
10[10]Georgeseu, A., Hydrodynamic Stability Theory, Martinus Nijhoff, Dordrecht, the Netherlands, 1985.

1苏煜城,沈全.半线性抛物型方程奇异摄动问题的数值解[J].应用数学和力学,1991,12(11):979-988.
2一类半线性抛物型方程初边值问题平衡解的不稳定性[J].天津教育学院学报（自然科学版）,1990(1):57-58.
3查中伟.半线性抛物型方程混合问题的爆破解[J].重庆三峡学院学报,2004,20(1):114-118.
4查中伟.半线性抛物型方程解的爆破问题[J].葛洲坝水电工程学院学报,1993,15(2):76-81.
5吴训青,肖美娟.半空间上非齐次半线性抛物型方程的可解性[J].湖南农业大学学报（自然科学版）,2010,36(S1):121-122.
6容跃堂,荔炜.半线性抛物型方程初边值问题解的性态[J].纯粹数学与应用数学,1992,8(2):21-26.
7张克农.Blow-up of Solutions of Semilinear Parabolic Equations*[J].Journal of Mathematical Research and Exposition,1993,13(3):327-336.
8查中伟.一类半线性抛物型方程解的爆破性质[J].西南师范大学学报（自然科学版）,2004,29(2):172-176. 被引量：4
9张勤,史佩鑫.一类半线性抛物型方程柯西问题全局解的渐近性态[J].郑州大学学报（理学版）,1996,32(S2):18-20.
10施国华.一类退化的半线性抛物方程解的爆破与全局存在性[J].南京大学学报（数学半年刊）,2000,17(1):116-124. 被引量：4

Northeastern Mathematical Journal

2000年第1期

浏览历史

内容加载中请稍等...

Longtime Convergence of Numerical Approximations for Semilinear Parabolic Equations (Ⅰ)

参考文献21

相关作者

相关机构

相关主题

浏览历史