Grid adaptation via node movement

Applied Numerical Mathematics

Volumn 26, Issue 1-2, 1998, Pages 77-96

  Baines, M J ^a  

^a UNIVERSITY OF READING   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; FUNCTIONS; ITERATIVE METHODS; OPTIMIZATION; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

ADAPTIVE GRID METHODS; ADVECTION EQUATION; DIRECT MINIMIZATION; EQUIDISTRIBUTION; MOVING FINITE ELEMENT METHOD; POISSON EQUATION; SHALLOW WATER EQUATION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0031644106     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(97)00085-8     Document Type: Article

References (16)

1. 2 fits to continuous functions with adjustable nodes in one and two dimensions, Math. Comp. 62 (1994) 645-669.
2. M.J. Baines, Moving Finite Elements (Oxford University Press, Oxford, 1994).
3. M.J. Baines, Approximate solutions of partial differential equations on optimal meshes using variational principles, Numerical Analysis Report 7/96, Department of Mathematics, University of Reading (1996).
4. 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.
5. G.F. Carey and H.T. Dinh, Grading functions and mesh redistribution, SIAM J. Numer. Anal. 22 (1985) 1028-1040.
6. C. de Boor, Good Approximation by Splines with Variable Knots II, Lecture Notes Series 363 (Springer, New York, 1973).
7. 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.
8. W. Huang and R.D. Russell, A high-dimensional moving mesh strategy, Appl. Numer. Math. 26 (1998) 63-76 (this issue).
9. M.E. Hubbard and M.J. Baines, Multidimensional upwinding and grid adaptation, in: K.W. Morton and M.J. Baines, eds., Numerical Methods for Fluid Dynamics V (Oxford University Press, Oxford, 1995) 431-438.
10. P.K. Jimack, A best approximation property of the moving finite element method, SIAM J. Numer. Anal. 33 (1996) 2286-2302.
11. C. Johnson and P. Hansbo, Adaptive finite element methods in computational mechanics. Comput. Methods Appl. Mech. Engrg. 101 (1992) 143-181.
12. E. Süli and P. Houston, Finite element methods for hyperbolic problems: stability, accuracy, adaptivity, Oxford University Computing Laboratory Report 96/09; also in: Proceedings of the IMA Conference on the State of the Art in Numerical Analysis, York, 1996 (OUP, to appear).
13. 2 approximation by discontinuous piecewise polynomials, Math. Comp. 66 (1997) 623-650.
14. S.L. Wakelin, Variational principles and the finite clement method for channel flows, Ph.D. Thesis, Department of Mathematics, University of Reading (1993).
15. S.L. Wakelin, MJ. Baines and D. Porter. The use of variational principles in determining approximations to continuous and discontinuous shallow water flows, Numerical Analysis Report 13/95, Department of Mathematics, University of Reading (1995).
16. P.A. Zegeling, MFE revisited, Part 1: Adaptive grid-generation using the heat equation, Preprint No. 946, Department of Mathematics, University of Utrecht (February, 1996).