Computational solution of two-dimensional unsteady PDEs using moving mesh methods

Journal of Computational Physics

Volumn 182, Issue 2, 2002, Pages 478-495

  Beckett, G ^a   Mackenzie, J A ^a   Ramage, A ^a   Sloan, D M ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Adaptivity; Equidistribution; Moving meshes

Indexed keywords

NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

ADAPTIVITY; COMPUTATIONAL SOLUTIONS; EQUIDISTRIBUTION; IMPORTANT FEATURES; MONITOR FUNCTIONS; MOVING MESH; MOVING MESH METHOD; NUMERICAL EXPERIMENTS; SPACE DIMENSIONS; TWO-DIMENSIONAL;

MESH GENERATION;

EID: 0036867839     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2002.7179     Document Type: Article

References (19)

1. O. Axelsson, Iterative Solution Methods (Cambridge Univ. Press, Cambridge, UK, 1994).
2. I. Babuška and W. C. Rheinboldt, A-posteriori error estimation for the finite element method, Int. J. Numer. Anal. Eng. 12, 1597 (1978).
3. M. J. Baines, Moving Finite Elements (Clarendon, Oxford, 1994).
4. G. Beckett and J. A. Mackenzie, Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem, Appl. Numer. Math. 35, 87 (2000).
5. G. Beckett and J. A. Mackenzie, On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution, J. Comput. Appl. Math. 131, 381 (2001).
6. G. Beckett and J. A. Mackenzie, Uniformly convergent high order finite element solutions of a singularly perturbed reaction-diffusion equation using mesh equidistribution, Appl. Numer. Math. 39, 31 (2001).
7. G. Beckett, J. A. Mackenzie, A. Ramage, and D. M. Sloan, On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution, J. Comput. Phys. 167, 372 (2001).
8. W. Cao, W. Huang, and R. D. Russell, A study of monitor functions for two-dimensional adaptive mesh generation, SIAM J. Sci. Comput. 20, 1978 (1999).
9. W. Cao, W. Huang, and R. D. Russell, An r-adaptive finite element method based upon moving mesh PDEs, J. Comput. Phys. 149, 221 (1999).
10. A. S. Dvinsky, Adaptive grid generation from harmonic maps on Reimannian manifolds, J. Comput. Phys. 95, 450 (1991).
11. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II (Springer-Verlag, New York, 1991).
12. W. Huang, Practical aspects of formulation and solution of moving mesh partial differential equations, J. Comput. Phys. 171, 753 (2001).
13. W. Huang and R. D. Russell, A high dimensional moving mesh strategy, Appl. Numer. Math. 26, 63 (1997).
14. W. Huang and R. D. Russell, Moving mesh strategy based on a gradient flow equation for two-dimensional problems, SIAM J. Sci. Comput. 20, 998 (1999).
15. R. Li, T. Tang, and P.-W. Zhang, A moving mesh finite element algorithm for singular problems in two and three space dimensions, J. Comput. Phys. 177, 365 (2002).
16. J. A. Meijerink and H. A. van der Vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comput. 31, 148 (1977).
17. K. Miller and R. N. Miller, Moving finite elements I, SIAM J. Numer. Anal. 18, 1019 (1981).
18. H. A. van der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 13, 631 (1992).
19. A. Winslow, Numerical solution of quasi-linear poisson equation in a nonuniform triangle mesh, J. Comput. Phys. 1, 149 (1967).