Solving parabolic problems using local defect correction in combination with the finite volume method

Numerical Methods for Partial Differential Equations

Volumn 22, Issue 5, 2006, Pages 1149-1172

  Minero, R ^a   Anthonissen, M J H ^a   Mattheij, R M M ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Composite grid; Finite volume methods; Global coarse grid; Local defect correction; Local fine grid

Indexed keywords

EID: 33748549604     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20143     Document Type: Article

References (15)

1. 1 W. Hackbusch, Local defect correction and domain decomposition techniques, K. Böhmer, H. J. Stetter editors, Defect Correction Methods. Theory and Applications, Computing, Suppl. 5 Springer, New York, 1984, pp. 89–113.
2. 2 P. J. J. Ferket, A. A. Reusken, Further analysis of the local defect correction method, Computing 56 ( 1996), 117–139.
3. 3 P. J. J. Ferket, A. A. Reusken, A finite difference discretization method on composite grids, Computing 56 ( 1996), 343–369.
4. 4 J. U. Wappler, Die lokale Defektkorrekturmethode zur adaptiven Diskretisierung elliptischer Differentialgleichungen mit finiten Elementen, PhD thesis, Christian‐Albrechts‐Universität, Kiel, 1999. (in German).
5. 5 V. Nefedov, R. M. M. Mattheij, Local defect correction with different grid types, Numer Methods Partial Differential Eq 18 ( 2002), 454–468.
6. 6 M. Graziadei, R. M. M. Mattheij, J. H. M. ten Thije Boonkkamp, Local defect correction with slanting grids, Numer Methods Partial Differential Eq 20 ( 2003), 1–17.
7. 7 R. Minero, M. J. H. Anthonissen, R. M. M. Mattheij, A local defect correction technique for time‐dependent problems, Numer Methods Partial Differential Eq 22 ( 2006), 128–144.
8. 8 M. J. H. Anthonissen, R. M. M. Mattheij, J. H. M. ten Thije Boonkkamp, Convergence analysis of the local defect correction method for diffusion equations, Numer Math 95 ( 2003), 401–425.
9. 9 M. J. H. Anthonissen, B. van 't Hof, A. A. Reusken, A finite volume scheme for solving elliptic boundary value problems on composite grids, Computing 61 ( 1998), 285–305.
10. 10 R. D. Lazarov, I. D. Mishev, P. S. Vassilevski, Finite volume methods with local refinement for convection‐diffusion problems, Computing 53 ( 1994), 33–57.
11. 11 C. Carstensen, R. D. Lazarov, S. Tomov, Explicit and averaging a posteriori error estimates for adaptive finite volume methods, SIAM J Numer Anal 42 ( 2005), 2496–2521.
12. 12 R. D. Lazarov, S. Tomov, A posteriori error estimates for finite volume element approximations of convection‐diffusion‐reaction equations, Comput Geosci 6 ( 2002), 483–503.
13. 13 M. Barad, P. Colella, A fourth‐order accurate local refinement method for Poisson's equation, J Comput Phys 209 ( 2005), 1–18.
14. 14 O. Roussel, K. Schneider, A. Tsigulin, H. Bockhorn, A conservative fully adaptive multiresolution algorithm for parabolic PDEs, J Comput Phys 188 ( 2003), 493–523.
15. 15 F. Bramkamp, P. Lamby, S. Müller, An adaptive multiscale finite volume solver for unsteady and steady state flow computations, J Comput Phys 197 ( 2004), 460–490.