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.

<strong>Adaptivity</strong> <strong>with</strong> <strong>moving</strong> <strong>grids</strong> 127<br />

differential equations in one space dimension’, Appl. Numer. Math. 5, 435–<br />

450.<br />

O.-P. Jacquotte (1988), ‘A mechanical model for a new grid generation method<br />

in computational fluid dynamics’, Comput. Methods Appl. Mech. Engrg 66,<br />

323–338.<br />

O.-P. Jacquotte and G. Coussement(1992), ‘Structured mesh adaption: Space<br />

accuracy and interpolation methods’, Comput. Methods Appl. Mech. Engrg<br />

101, 397–432.<br />

C. Johnson (1987), Numerical Solution of Partial Differential Equations by the<br />

Finite Element Method, Cambridge University Press.<br />

T. Kaijser (1998), ‘Computing the Kantorovich distance for images’, J. Math. Imaging<br />

Vision 9, 173–191.<br />

J. Kautsky and N. K. Nichols (1980), ‘Equidistributing meshes <strong>with</strong> constraints’,<br />

SIAM J. Sci. Statist. Comput. 1, 499–511.<br />

J. Kautsky and N. K. Nichols (1982), ‘Smooth regrading of discretized data’,<br />

SIAM J. Sci. Statist. Comput. 3, 145–159.<br />

P. M. Knupp (1995), ‘Mesh generation using vector fields’, J. Comput. Phys.<br />

119, 142–148.<br />

P. M. Knupp (1996), ‘Jacobian-weighted elliptic grid generation’, SIAM J. Sci.<br />

Comput. 17, 1475–1490.<br />

P. M. Knupp (2001), ‘Algebraic mesh quality metrics’, SIAM J. Sci. Comput.<br />

23, 193–218.<br />

P. Knupp and N. Robidoux (2000), ‘A framework for variational grid generation:<br />

Conditioning the Jacobian matrix <strong>with</strong> matrix norms’, SIAM J. Sci. Comput.<br />

21, 2029–2047.<br />

P. Knupp and S. Steinberg (1994), Fundamentals of Grid Generation, CRC Press,<br />

Boca Raton.<br />

P. M. Knupp, L. Margolin and M. Shashkov (2002), ‘Reference Jacobian optimization-based<br />

rezoning strategies for arbitrary Lagrangian Eulerian methods’,<br />

J. Comput. Phys. 176, 93–128.<br />

N. Kopteva (2007), Convergence theory of <strong>moving</strong> grid methods, in Adaptive Computations:<br />

Theory and Algorithms (T. Tang and J. Xu, eds), Science Press,<br />

Beijing, pp. 159–210.<br />

N. Kopteva and M. Stynes (2001), ‘A robust adaptive method for a quasilinear onedimensional<br />

convection–diffusion problem’, SIAM J. Numer. Anal. 39, 1446–<br />

1467.<br />

R. Kozlov (2000), Symmetry applications to difference and differential-difference<br />

equations. PhD Thesis, Institut for matematiske fag, NTNU, Trondheim.<br />

J. Lang, W. Cao, W. Huang and R. D. Russell (2003), ‘A two-dimensional <strong>moving</strong><br />

finite element method <strong>with</strong> local refinement based on a posteriori error<br />

estimates’, Appl. Numer. Math. 46, 75–94.<br />

G. Lapenta and L. Chacón (2006), ‘Cost-effectiveness of fully implicit <strong>moving</strong> mesh<br />

adaptation: A practical investigation in 1D’, J. Comput. Phys. 219, 86–103.<br />

R. J. LeVeque (1990), Numerical Methods for Conservation Laws, Birkhäuser.<br />

R. Li, T. Tang, and P.-W. Zhang (2002), ‘A <strong>moving</strong> mesh finite element algorithm<br />

for singular problems in two and three space dimensions’, J. Comput. Phys.<br />

177, 365–393.

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

Saved successfully!

Ooh no, something went wrong!