26.12.2013 Views

Adaptivity with moving grids

Adaptivity with moving grids

Adaptivity with moving grids

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

Acknowledgements<br />

<strong>Adaptivity</strong> <strong>with</strong> <strong>moving</strong> <strong>grids</strong> 121<br />

It is a pleasure to thank Emily Walsh for Figures 5.7, 5.8, 5.9, 5.11 and 5.12<br />

and J. F. Williams for Figures 3.7, 3.8, 3.9, 3.11, 5.2 and 5.4. Both also<br />

helped by reading this text and through many useful discussions. This work<br />

was supported in part by the EPSRC Critical Mass Grant GR/586525/01.<br />

REFERENCES<br />

S. Adjerid and J. E. Flaherty (1986), ‘A <strong>moving</strong> finite element method <strong>with</strong> error<br />

estimation and refinement for one-dimensional time dependent partial differential<br />

equations’, SIAM J. Numer. Anal. 23, 778–795.<br />

M. Ainsworth and J. T. Oden (2000), A Posteriori Error Estimation in Finite<br />

Element Analysis, Pure and Applied Mathematics, Wiley-Interscience.<br />

V. F. Almeida (1999), ‘Domain deformation mapping: Application to variational<br />

mesh generation’, SIAM J. Sci Comput. 20, 1252–1275.<br />

D. A. Anderson and M. M. Rai (1983), The use of solution adaptive <strong>grids</strong> in solving<br />

partial differential equations, in Numerical Grid Generation (J. H. Thompson,<br />

ed.), pp. 317–338.<br />

V. B. Andreev and N. B. Kopteva (1998), ‘On the convergence, uniform <strong>with</strong><br />

respect to a small parameter, of monotone three-point difference approximations’,<br />

Diff. Urav. 34, 921–929.<br />

U. Ascher, J. Christiansen and R. D. Russell (1981), ‘Collocation software for<br />

boundary value ODEs’, ACM Trans. Math. Software 7, 209–222.<br />

I. Babuška and W. C. Rheinboldt (1979), ‘Analysis of optimal finite element meshes<br />

in R 1 ’, Math. Comput. 33, 435–463.<br />

M. J. Baines (1994), Moving Finite Elements, Clarendon Press, Oxford.<br />

M. J. Baines and S. L. Wakelin (1991), Equidistribution and the Legendre transformation.<br />

Numerical Analysis report 4/91, University of Reading.<br />

M. J. Baines, M. E. Hubbard, and P. K. Jimack (2005), ‘A <strong>moving</strong> mesh finite strategy<br />

for the adaptive solution of time-dependent partial differential equations<br />

<strong>with</strong> <strong>moving</strong> boundaries’, Appl. Numer. Math. 54, 450–469.<br />

M. J. Baines, M. E. Hubbard, P. K. Jimack, and A. C. Jones (2006), ‘Scaleinvariant<br />

<strong>moving</strong> finite elements for nonlinear partial differential equations in<br />

two dimensions’, Appl. Numer. Math. 56, 230–252.<br />

M. L. Balinski (1986), ‘A competitive (dual) simplex method for the assignment<br />

problem’, Math. Program. 34, 125–141.<br />

R. E. Bank and R. K. Smith (1997), ‘Mesh smoothing using a posteriori error<br />

estimates’, SIAM J. Numer. Anal. 34, 979–997.<br />

G. I. Barenblatt (1996), Scaling, Self-Similarity, and Intermediate Asymptotics:<br />

Dimensional Analysis and Intermediate Asymptotics, Cambridge Texts in Applied<br />

Mathematics, Cambridge University Press.<br />

G. Beckett and J. A. Mackenzie (2000), ‘Convergence analysis of finite-difference<br />

approximations on equidistributed <strong>grids</strong> to a singularly perturbed boundary<br />

value problem’, Appl. Numer. Math. 35, 87–109.<br />

G. Beckett and J. A. Mackenzie (2001a), ‘On a uniformly accurate finite difference<br />

approximation of a singularly perturbed reaction–diffusion problem using grid<br />

equidistribution’, J. Comput. Appl. Math. 131, 381–405.

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!