- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 413718, 19 pages
A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations
School of Mathematics, Shandong University, Jinan 250100, China
Received 1 September 2012; Accepted 14 November 2012
Academic Editor: Xinan Hao
Copyright © 2012 Tongjun Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- K. Miller and R. N. Miller, “Moving finite elements. I,” SIAM Journal on Numerical Analysis, vol. 18, no. 6, pp. 1019–1032, 1981.
- K. Miller, “Moving finite elements. II,” SIAM Journal on Numerical Analysis, vol. 18, no. 6, pp. 1033–1057, 1981.
- G. P. Liang and Z. M. Chen, “A full-discretization moving FEM with optimal convergence rate,” Chinese Journal of Numerical Mathematics and Applications, vol. 12, no. 4, pp. 91–111, 1990.
- D. Q. Yang, “The mixed finite-element methods with moving grids for parabolic problems,” Mathematica Numerica Sinica, vol. 10, no. 3, pp. 266–271, 1988.
- H. L. Song and Y. R. Yuan, “An upwind-mixed method on changing meshes for two-phase miscible flow in porous media,” Applied Numerical Mathematics, vol. 58, no. 6, pp. 815–826, 2008.
- G. I. Barenblatt, I. P. Zheltov, and I. N. Kochina, “Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks,” Journal of Applied Mathematics and Mechanics, vol. 24, no. 5, pp. 1286–1303, 1960.
- D. M. Shi, “The initial-boundary value problem for a nonlinear equation of migration of moisture in soil,” Acta Mathematicae Applicatae Sinica, vol. 13, no. 1, pp. 31–38, 1990.
- T. W. Ting, “A cooling process according to two-temperature theory of heat conduction,” Journal of Mathematical Analysis and Applications, vol. 45, pp. 23–31, 1974.
- R. E. Ewing, “Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations,” SIAM Journal on Numerical Analysis, vol. 15, no. 6, pp. 1125–1150, 1978.
- J. Zhu, “Finite element methods for nonlinear Sobolev equations,” Northeastern Mathematical Journal, vol. 5, no. 2, pp. 179–196, 1989.
- T. J. Sun and K. Y. Ma, “Finite difference-streamline diffusion method for quasi-linear Sobolev equations,” Numerical Mathematics, vol. 23, no. 4, pp. 340–356, 2001.
- T. J. Sun and D. P. Yang, “Error estimates for a discontinuous Galerkin method with interior penalties applied to nonlinear Sobolev equations,” Numerical Methods for Partial Differential Equations, vol. 24, no. 3, pp. 879–896, 2008.
- J. S. Zhang, D. P. Yang, and J. Zhu, “Two new least-squares mixed finite element procedures for convection-dominated Sobolev equations,” Applied Mathematics, vol. 26, no. 4, pp. 401–411, 2011.
- C. Chavent and J. Jaffer, Mathematical Models and Finite Elements for Reservoir Simulation, North Holland, Amsterdam, The Netherlands, 1996.
- J. B. Bell, C. N. Dawson, and G. R. Shubin, “An unsplit, higher order godunov method for scalar conservation laws in multiple dimensions,” Journal of Computational Physics, vol. 74, no. 1, pp. 1–24, 1988.
- C. N. Dawson, “Godunov-mixed methods for immiscible displacement,” International Journal for Numerical Methods in Fluids, vol. 11, no. 6, pp. 835–847, 1990.
- J. B. Bell, P. Colella, and H. M. Glaz, “A second-order projection method for the incompressible Navier-Stokes equations,” Journal of Computational Physics, vol. 85, no. 2, pp. 257–283, 1989.
- C. N. Dawson, “Godunov-mixed methods for advective flow problems in one space dimension,” SIAM Journal on Numerical Analysis, vol. 28, no. 5, pp. 1282–1309, 1991.
- C. Dawson, “Godunov-mixed methods for advection-diffusion equations in multidimensions,” SIAM Journal on Numerical Analysis, vol. 30, no. 5, pp. 1315–1332, 1993.
- T. Arbogast, M. F. Wheeler, and I. Yotov, “Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences,” SIAM Journal on Numerical Analysis, vol. 34, no. 2, pp. 828–852, 1997.
- P. A. Raviart and J. M. Thomas, “A mixed finite element method for 2nd order elliptic problems,” in Mathematical Aspects of the Finite Element Methods, vol. 606 of Lecture Notes in Mathematics, pp. 292–315, Springer, Berlin, Germany, 1977.
- J. Douglas, Jr. and J. E. Roberts, “Global estimates for mixed methods for second order elliptic equations,” Mathematics of Computation, vol. 44, no. 169, pp. 39–52, 1985.