Free Access
Issue
ESAIM: M2AN
Volume 42, Number 3, May-June 2008
Page(s) 443 - 469
DOI https://doi.org/10.1051/m2an:2008012
Published online 03 April 2008
  1. P.F. Antonietti and B. Ayuso, Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: Non-overlapping case. ESAIM: M2AN 41 (2007) 21–54. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  2. P.F. Antonietti, A. Buffa and I. Perugia, Discontinuous Galerkin approximation of the Laplace eigenproblem. Comput. Methods Appl. Mech. Engrg. 195 (2006) 3483–3503. [Google Scholar]
  3. D.N. Arnold, An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 (1982) 742–760. [CrossRef] [MathSciNet] [Google Scholar]
  4. D.N. Arnold, F. Brezzi, B. Cockburn and L.D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2001) 1749–1779 (electronic). [Google Scholar]
  5. F. Bassi and S. Rebay, A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 131 (1997) 267–279. [CrossRef] [MathSciNet] [Google Scholar]
  6. F. Bassi, S. Rebay, G. Mariotti, S. Pedinotti and M. Savini, A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows, in Proceedings of the 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, R. Decuypere and G. Dibelius Eds., Technologisch Instituut, Antwerpen, Belgium (1997) 99–108. [Google Scholar]
  7. C.E. Baumann and J.T. Oden, A discontinuous hp finite element method for convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 175 (1999) 311–341. [CrossRef] [MathSciNet] [Google Scholar]
  8. J.H. Bramble, J.E. Pasciak, J.P. Wang and J. Xu, Convergence estimates for product iterative methods with applications to domain decomposition. Math. Comp. 57 (1991) 1–21. [CrossRef] [MathSciNet] [Google Scholar]
  9. S.C. Brenner and O. Luke, A W-cycle algorithm for a weakly over-penalized interior penalty method. JNAIAM J. Numer. Anal. Indust. Appl. Math 196 (2007) 3823–3832. [Google Scholar]
  10. S.C. Brenner and O. Luke, A weakly over-penalized non-symmetric Interior Penalty method. Comput. Methods Appl. Mech. Engrg. 2 (2007) 35–48. [Google Scholar]
  11. S.C. Brenner and L.-Y. Sung, Multigrid algorithms for C0 interior penalty methods. SIAM J. Numer. Anal. 44 (2006) 199–223 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  12. S.C. Brenner and K. Wang, Two-level additive Schwarz preconditioners for C0 interior penalty methods. Numer. Math. 102 (2005) 231–255. [CrossRef] [MathSciNet] [Google Scholar]
  13. S.C. Brenner and J. Zhao, Convergence of multigrid algorithms for interior penalty methods. Appl. Numer. Anal. Comput. Math. 2 (2005) 3–18. [CrossRef] [MathSciNet] [Google Scholar]
  14. F. Brezzi, G. Manzini, D. Marini, P. Pietra and A. Russo, Discontinuous Galerkin approximations for elliptic problems. Numer. Methods Partial Differential Equations 16 (2000) 365–378. [Google Scholar]
  15. X.-C. Cai and O.B. Widlund, Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems. SIAM J. Numer. Anal. 30 (1993) 936–952. [CrossRef] [MathSciNet] [Google Scholar]
  16. P.G. Ciarlet, The Finite Element Method for Elliptic Problems, Studies in Mathematics and its Applications 4. North-Holland Publishing Co., Amsterdam (1978). [Google Scholar]
  17. B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35 (1998) 2440–2463 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  18. C. Dawson, S. Sun and M.F. Wheeler, Compatible algorithms for coupled flow and transport. Comput. Methods Appl. Mech. Engrg. 193 (2004) 2565–2580. [Google Scholar]
  19. V.A. Dobrev, R.D. Lazarov, P.S. Vassilevski and L.T. Zikatanov, Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations. Numer. Linear Algebra Appl. 13 (2006) 753–770. [CrossRef] [MathSciNet] [Google Scholar]
  20. J. Douglas, Jr. and T. Dupont, Interior penalty procedures for elliptic and parabolic Galerkin methods, in Computing Methods in Applied Sciences (Second Internat. Sympos., Versailles, 1975), Lecture Notes in Physics 58, Springer, Berlin (1976) 207–216. [Google Scholar]
  21. S.C. Eisenstat, H.C. Elman and M.H. Schultz, Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 20 (1983) 345–357. [CrossRef] [MathSciNet] [Google Scholar]
  22. X. Feng and O.A. Karakashian, Two-level additive Schwarz methods for a discontinuous Galerkin approximation of second order elliptic problems. SIAM J. Numer. Anal. 39 (2001) 1343–1365 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  23. G.H. Golub and C.F. Van Loan, Matrix Computations. 3rd Edn., Johns Hopkins University Press, Baltimore, USA (1996). [Google Scholar]
  24. J. Gopalakrishnan and G. Kanschat, A multilevel discontinuous Galerkin method. Numer. Math. 95 (2003) 527–550. [CrossRef] [MathSciNet] [Google Scholar]
  25. G. Kanschat, Preconditioning methods for local discontinuous Galerkin discretizations. SIAM J. Sci. Comput. 25 (2003) 815–831 (electronic). [CrossRef] [Google Scholar]
  26. G. Kanschat, Block preconditioners for LDG discretizations of linear incompressible flow problems. J. Sci. Comput. 22/23 (2005) 371–384. [Google Scholar]
  27. C. Lasser and A. Toselli, An overlapping domain decomposition preconditioner for a class of discontinuous Galerkin approximations of advection-diffusion problems. Math. Comp. 72 (2003) 1215–1238 (electronic). [Google Scholar]
  28. P.-L. Lions, On the Schwarz alternating method. I, in First International Symposium on Domain Decomposition Methods for Partial Differential Equations (Paris, 1987), SIAM, Philadelphia, PA (1988) 1–42. [Google Scholar]
  29. M. Murillo and X.-C. Cai, A fully implicit parallel algorithm for simulating the non-linear electrical activity of the heart. Numer. Linear Algebra Appl. 11 (2004) 261–277. [CrossRef] [Google Scholar]
  30. L.F. Pavarino and S. Scacchi, Multilevel Schwarz and multigrid preconditioners for the bidomain system, in Domain Decomposition Methods in Science and Engineering XVII, U. Langer, M. Discacciati, D. Keyes, O. Widlund and W. Zulehner Eds., Lecture Notes in Computational Science and Engineering 60, Springer, Heidelberg (2008) 631–638. [Google Scholar]
  31. L.F. Pavarino and A. Toselli, Recent Developments in Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering 23. Springer-Verlag, Berlin (2002). [Selected papers from the Workshop on Domain Decomposition held at ETH Zürich, Zürich, June 7–8 (2001)]. [Google Scholar]
  32. W.H. Reed and T. Hill, Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory, USA (1973). [Google Scholar]
  33. B. Rivière, M.F. Wheeler and V. Girault, Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I. Comput. Geosci. 3 (1999) 337–360. [CrossRef] [Google Scholar]
  34. V. Simoncini and D.B. Szyld, New conditions for non-stagnation of minimal residual methods. Technical Report 07-04-17, Department of Mathematics, Temple University, USA (2007), to appear in Numerische Mathematik. [Google Scholar]
  35. B.F. Smith, P.E. Bjørstad and W.D. Gropp, Domain decomposition. Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, Cambridge (1996). [Google Scholar]
  36. R. Stenberg, Mortaring by a method of J.A. Nitsche, in Computational mechanics (Buenos Aires, 1998), Centro Internac. Métodos Numér. Ing., Barcelona, Spain (1998). [Google Scholar]
  37. A. Toselli and O. Widlund, Domain Decomposition Methods—Algorithms and Theory, Springer Series in Computational Mathematics 34. Springer-Verlag, Berlin (2005). [Google Scholar]
  38. J. Xu, Iterative methods by space decomposition and subspace correction. SIAM Rev. 34 (1992) 581–613. [CrossRef] [MathSciNet] [Google Scholar]
  39. J. Xu, Iterative methods by SPD and small subspace solvers for nonsymmetric or indefinite problems, in Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations (Norfolk, VA, 1991), SIAM, Philadelphia, PA (1992) 106–118. [Google Scholar]
  40. J. Xu, A new class of iterative methods for nonselfadjoint or indefinite problems. SIAM J. Numer. Anal. 29 (1992) 303–319. [CrossRef] [Google Scholar]
  41. J. Xu and L. Zikatanov, The method of alternating projections and the method of subspace corrections in Hilbert space. J. Amer. Math. Soc. 15 (2002) 573–597 (electronic). [CrossRef] [Google Scholar]

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