# A moving mesh method with variable relaxation time

- Published: 17 Feb 2006

- Simon Fraser University Canada
- University of Sistan and Baluchestan Iran (Islamic Republic of)

- Funder: Natural Sciences and Engineering Research Council of Canada (NSERC)

- 1
- 2

[1] S. Adjerid and J. E. Flaherty, A moving-mesh finite element method with local refinement for parabolic partial differential equations, Comput. Meth. Appl. Mech. Engrg. 55 (1986) 3-26. [OpenAIRE]

[2] U. M. Ascher, DAEs that should not be solved, in: R. de la Llave, . R. Petzold and J. Lorenz (Eds.), Dynamics of Algorithms, IMA Proceedings Vol. 118, 1999, pp. 55-68.

[3] M. J. Baines, M. E. Hubbard, P. K. Jimack and A. C. Jones, Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions, Appl. Numer. Math. (2006) in press. [OpenAIRE]

[4] J. Bebernes and S. Bricher, Final time blowup profiles for semilinear parabolic equations via center manifold theory, SIAM J. Math. Anal. 23 (1992) 852-869.

[5] C. J. Budd, R. Carretero-Gonza´lez and R. D. Russell, Precise computations of chemotactic collapse using moving mesh methods, J. Comput. Phys. 202 (2005) 463-487.

[6] C. J. Budd, J. Chen, W. Huang, and R. D. Russell, Moving mesh methods with applications to blow-up problems for PDEs, in: D. F. Griffiths and G. A. Watson (Eds.), Proceedings of 1995 Biennial Conference on Numerical Analysis, Pitman Research Notes in Mathematics Vol. 344, Addison Wesley, 1996, pp. 1-17.

[7] C. J. Budd, W. Huang and R. D. Russell, Moving mesh methods for problems with blow-up, SIAM J. Sci. Comput. 17 (1996) 305-327.

[8] C. J. Budd, B. Leimkuhler and M. D. Piggott, Scaling invariance and adaptivity, Appl. Numer. Math. 39 (2001) 261-288.

[9] Neil N. Carlson and Keith Miller, Design and application of a gradient-weighted moving finite element code. I: In one dimension, SIAM J. Sci. Comput. 19 (1998) 728-765.

[10] J. Coyle, J. Flaherty and R. Ludwig, On the stability of mesh equidistribution strategies for time-dependent partial differential equations, J. Comput. Phys. 62 (1986) 26-39.

[11] A. Friedman and B. McLeod, Blowup of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985) 425-447.

[12] J. M. Hyman and B. Larrouturou, Dynamic rezone methods for partial differential equations in one space dimension, Appl. Numer. Math. 5 (1986) 435-450.

[13] W. Huang, Y. Ren and R. D. Russell, Moving mesh methods based on moving mesh partial differential equations, J. Comput. Phys. 113 (1994) 279-290.

[14] W. Huang, Y. Ren and R. D. Russell, Moving mesh partial differential equations (MMPDEs) based on the equidistribution principle, SIAM J. Numer. Anal. 31 (1994) 709-730.

[15] W. Huang, Practical aspects of formulation and solution of moving mesh partial differential equations, J. Comput. Phys. 171 (2001) 753-775.

- 1
- 2