EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 48 / No 5 (September-October 2014) ESAIM: M2AN, 48 5 (2014) 1473-1494 References
Free Access
Issue
ESAIM: M2AN
Volume 48, Number 5, September-October 2014
Page(s) 1473 - 1494
DOI https://doi.org/10.1051/m2an/2014006
Published online 13 August 2014
  1. J.H. Adler, J. Brannick, C. Liu, T. Manteuffel and L. Zikatanov, First-order system least squares and the energetic variational approach for two-phase flow. J. Comput. Phys. 230 (2011) 6647–6663. [CrossRef] [Google Scholar]
  2. J.H. Adler, T.A. Manteuffel, S.F. McCormick, J.W. Nolting, J.W. Ruge and L. Tang, Efficiency based adaptive local refinement for first-order system least-squares formulations. SIAM J. Sci. Comput. 33 (2011) 1–24. [CrossRef] [Google Scholar]
  3. A. Barker, S. Brenner, E.-H. Park and L-Y. Sung, A one-level additive schwarz preconditioner for a discontinuous petrov-galerkin method. Preprint arXiv:1212.2645 (2012). To appear in the Proceeding of DD21. [Google Scholar]
  4. P.B. Bochev and M.D. Gunzburger, Finite element methods of least-squares type. SIAM Rev. 40 (1998) 789–837. [CrossRef] [MathSciNet] [Google Scholar]
  5. P.B. Bochev and M.D. Gunzburger, Least-Squares Finite Element Methods, vol. 166 of Appl. Math. Sci. Springer, New York (2009). [Google Scholar]
  6. D. Braess, Finite Elements. Theory, fast solvers, and applications in solid mechaics. 3th ed. Cambridge University Press (2007). [Google Scholar]
  7. J.H. Bramble, R.D. Lazarov and J.E. Pasciak, A least-squares approach based on a discrete minus one inner product for first order systems. Math. Comput. 66 (1997) 935–955. [CrossRef] [Google Scholar]
  8. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer (1991). [Google Scholar]
  9. T. Bui-Thanh, L. Demkowicz and O. Ghattas, A Unified Discontinuous Petrov−Galerkin Method and its Analysis for Friedrichs’ Systems. SIAM J. Numer. Anal. 51 (2013) 1933–1956. [CrossRef] [Google Scholar]
  10. A. Buffa and P. Monk, Error estimates for the ultra weak variational formulation of the Helmholtz equation. Math. Model. Numer. Anal. 42 (2008) 925–940. [Google Scholar]
  11. Z. Cai, R. Lazarov, T.A. Manteuffel and S.F. McCormick, First-Order System Least Squares for Second-Order Partial Differential Equations: Part I. SIAM J. Numer. Anal. 31 (1994) 1785–1799. [CrossRef] [Google Scholar]
  12. J. Chan, L. Demkowicz and N. Heuer, Robust DPG method for convection-dominated diffusion problems II: Natural inflow condition. Comput. Math. Appl. 67 (2014) 771–795. [CrossRef] [Google Scholar]
  13. W. Dahmen, C. Huang, C. Schwab and G. Welper, Adaptive Petrov-Galerkin methods for first order transport equations. SIAM J. Numer. Anal. 50 (2012) 2420–2445. [CrossRef] [Google Scholar]
  14. W. Dahmen, C. Plesken and G. Welper, Double greedy algorithms: reduced basis methods for transport dominated problems (2013). Preprint arXiv:1302.5072. [Google Scholar]
  15. L. Demkowicz and J. Gopalakrishnan, Analysis of the DPG method for the Poisson equation. SIAM J. Numer. Anal. 49 (2011) 1788–1809. [CrossRef] [Google Scholar]
  16. L. Demkowicz, J. Gopalakrishnan, I. Muga and J. Zitelli, Wavenumber explicit analysis for a DPG method for the multidimensional Helmholtz equation. Comput. Methods Appl. Mech. Engrg. 213 (2012) 126–138. [CrossRef] [MathSciNet] [Google Scholar]
  17. L. Demkowicz, J. Gopalakrishnan and A.H. Niemi, A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity. Appl. Numer. Math. 62 (2012) 396–427. [CrossRef] [Google Scholar]
  18. L. Demkowicz and N. Heuer, Robust DPG method for convection-dominated diffusion problems. SIAM J. Numer. Anal. 51 (2013) 2514–2537. [CrossRef] [Google Scholar]
  19. S. Esterhazy and J.M. Melenk, On stability of discretizations of the Helmholtz equation, in Numerical Analysis of Multiscale Problems, vol. 83 of Lect. Notes Comput. Sci. Engrg. Springer, Berlin (2012) 285–324. [Google Scholar]
  20. J. Gopalakrishnan and W. Qiu, An analysis of the practical DPG method. Math. Comput. (2013). [Google Scholar]
  21. I. Herrera, Trefftz method: A general theory. Numer. Methods Partial Differ. Eqs. 16 (2000) 561–580. [Google Scholar]
  22. J.J. Heys, E. Lee, T.A. Manteuffel, S.F. Mccormick and J.W. Ruge, Enhanced mass conservation in least-squares methods for Navier-Stokes equations. SIAM J. Sci. Comput. 31 (2009) 2303–2321. [CrossRef] [Google Scholar]
  23. R. Hiptmair, A. Moiola and I. Perugia, Stability results for the time-harmonic Maxwell equations with impedance boundary conditions. Math. Models Methods Appl. Sci. 21 (2011) 2263–2287. [Google Scholar]
  24. R. Hiptmair and J. Xu, Nodal auxiliary space preconditioning in H(curl) and H(div) spaces. SIAM J. Numer. Anal. 45 (2007) 2483–2509. [CrossRef] [MathSciNet] [Google Scholar]
  25. B.N. Khoromskij and G. Wittum, Numerical solution of elliptic differential equations by reduction to the interface. Berlin, Springer (2004). [Google Scholar]
  26. W. Krendl, V. Simoncini and W. Zulehner, Stability Estimates and Structural Spectral Properties of Saddle Point Problems. Numer. Math. 124 (2013) 183–213. [CrossRef] [MathSciNet] [Google Scholar]
  27. U. Langer, G. Of, O. Steinbach and W. Zulehner, Inexact data-sparse boundary element tearing and interconnecting methods. SIAM J. Sci. Comput. 29 (2007) 290–314. [CrossRef] [MathSciNet] [Google Scholar]
  28. J.M. Melenk, On generalized finite element methods. Ph.D. thesis, University of Maryland (1995). [Google Scholar]
  29. A. Moiola, Trefftz-Discontinuous Galerkin Methods for Time-Harmonic Wave Problems. Ph.D. thesis, ETH Zürich (2011). [Google Scholar]
  30. N. Roberts, T. Bui-Thanh and L. Demkowicz. The DPG method for the Stokes problem ICES Report (2012) 12–22. [Google Scholar]
  31. D.B. Szyld, The many proofs of an identity on the norm of oblique projections. Numer. Algorithms 42 (2006) 309–323. [CrossRef] [MathSciNet] [Google Scholar]
  32. C. Wieners, A geometric data structure for parallel finite elements and the application to multigrid methods with block smoothing. Comput. Visual. Sci. 13 (2010) 161–175. [CrossRef] [Google Scholar]
  33. J. Xu and L. Zikatanov, Some observations on Babuška and Brezzi theories. Numer. Math. 94 (2003) 195–202. [CrossRef] [MathSciNet] [Google Scholar]
  34. J. Zitelli, I. Muga, L. Demkowicz, J. Gopalakrishnan, D. Pardo and V. Calo, A class of discontinuous Petrov−Galerkin methods. Part IV: Wave propagation. J. Comput. Phys. 230 (2011) 2406–2432. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you