论文信息 - Numerical methods for the rosenau equation

Numerical methods for the rosenau equation

In this paper, a continuous in time finite element Galerkin method is first discussed for a KdV-like Rosenau equation in several space variables and optimal error estimates in L2, H1 as well as in H2- norms are derived for conforming C1-finite element spaces. Finally, several fully discrete schemes like backward Euler, Crank-Nicolson and two step backward methods are proposed and related convergence results are established.

Amiya K. Pani | A. K. Pani | Sank K. Chunk

[1] S. Ha,et al. Finite element galerkin solutions for the rosenau equation , 1994 .

[2] Mi Ai Park. On the Rosenau equation in multidimensional space , 1993 .

[3] C. M. Elliott,et al. A nonconforming finite-element method for the two-dimensional Cahn-Hilliard equation , 1989 .

[4] Philippe G. Ciarlet,et al. The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[5] M. Wheeler. A Priori L_2 Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations , 1973 .

[6] Philip Rosenau,et al. Dynamics of Dense Discrete Systems High Order Effects , 1988 .

[7] Milton Lees. Approximate Solutions of Parabolic Equations , 1959 .

[8] J. Douglas,et al. A family of $C^1$ finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems , 1979 .

[9] Vidar Thomée,et al. Numerical solution of an evolution equation with a positive-type memory term , 1993, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[10] Xuejun Zhang. Two-level Schwarz methods for the biharmonic problem discretized by conforming C 1 elements , 1996 .