Free Access
Volume 48, Number 3, May-June 2014
Page(s) 727 - 752
Published online 11 February 2014
  1. 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 (2002) 1749–1779. [CrossRef] [MathSciNet] [Google Scholar]
  2. I. Babuška and B.Q. Guo, The h-p version of the finite element method for domains with curved boundaries. SIAM J. Numer. Anal. 25 (1988) 837–861. [CrossRef] [Google Scholar]
  3. I. Babuška and B.Q. Guo, Regularity of the solution of elliptic problems with piecewise analytic data. I. Boundary value problems for linear elliptic equation of second order. SIAM J. Math. Anal. 19 (1988) 172–203. [CrossRef] [MathSciNet] [Google Scholar]
  4. I. Babuška and B.Q. Guo, The h-p version of the finite element method for problems with nonhomogeneous essential boundary condition. Comput. Methods Appl. Mech. Engrg. 74 (1989) 1–28. [CrossRef] [MathSciNet] [Google Scholar]
  5. I. Babuška and B.Q. Guo, Regularity of the solution of elliptic problems with piecewise analytic data. II. The trace spaces and application to the boundary value problems with nonhomogeneous boundary conditions. SIAM J. Math. Anal. 20 (1989) 763–781. [CrossRef] [MathSciNet] [Google Scholar]
  6. G.A. Baker, Finite element methods for elliptic equations using nonconforming elements. Math. Comput. 31 (1977) 45–59. [CrossRef] [MathSciNet] [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. O. Cessenat and B. Després, Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz equation. SIAM J. Numer. Anal. 35 (1998) 255–299. [CrossRef] [MathSciNet] [Google Scholar]
  9. P.J. Davis, Interpolation and approximation, Republication, with minor corrections, of the 1963 original, with a new preface and bibliography. Dover Publications Inc., New York (1975). [Google Scholar]
  10. 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), Vol. 58. Lect. Notes in Phys. Springer, Berlin (1976) 207–216. [Google Scholar]
  11. T.A. Driscoll and L.N. Trefethen, Schwarz-Christoffel mapping, in vol. 8 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge (2002). [Google Scholar]
  12. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL (1992). [Google Scholar]
  13. C. Farhat, I. Harari and U. Hetmaniuk, A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime. Comput. Methods Appl. Mech. Eng. 192 (2003) 1389–1419. [CrossRef] [Google Scholar]
  14. G. Gabard, P. Gamallo and T. Huttunen, A comparison of wave-based discontinuous Galerkin, ultra-weak and least-square methods for wave problems. Int. J. Numer. Methods Engrg. 85 (2011) 380–402. [CrossRef] [Google Scholar]
  15. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Classics in Mathematics, 2nd edition. Springer-Verlag (1983). [Google Scholar]
  16. P. Grisvard, Elliptic problems in nonsmooth domains, in vol. 24 of Monogr. Stud. Math. Pitman, Boston (1985). [Google Scholar]
  17. P. Henrici, Applied and computational complex analysis, Power series-integration-conformal mapping-location of zeros, in vol. 1 of Pure and Applied Mathematics. John Wiley & Sons, New York (1974). [Google Scholar]
  18. P. Henrici, Applied and computational complex analysis, Discrete Fourier analysis-Cauchy integrals-construction of conformal maps-univalent functions, in vol. 3 of Pure and Applied Mathematics. John Wiley & Son, New York (1986). [Google Scholar]
  19. R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version. SIAM J. Numer. Anal. 49 (2011) 264–284. [CrossRef] [MathSciNet] [Google Scholar]
  20. R. Hiptmair, A. Moiola and I. Perugia, Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes. Appl. Numer. Math. (2013). Available at [Google Scholar]
  21. R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version, Technical report 2013-31 (, SAM-ETH Zürich, Switzerland (2013). Submitted to Found. Comput. Math. [Google Scholar]
  22. R. Hiptmair, A. Moiola, I. Perugia and C. Schwab, Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM, Technical report 2012-38 (, SAM-ETH, Zürich, Switzerland (2012). [Google Scholar]
  23. T. Huttunen, P. Monk and J. P. Kaipio, Computational aspects of the ultra-weak variational formulation. J. Comput. Phys. 182 (2002) 27–46. [CrossRef] [MathSciNet] [Google Scholar]
  24. F. Li, On the negative-order norm accuracy of a local-structure-preserving LDG method. J. Sci. Comput. 51 (2012) 213–223. [CrossRef] [Google Scholar]
  25. F. Li and C.-W. Shu, A local-structure-preserving local discontinuous Galerkin method for the Laplace equation. Methods Appl. Anal. 13 (2006) 215–233. [CrossRef] [MathSciNet] [Google Scholar]
  26. A.I. Markushevich, Theory of functions of a complex variable. Vol. I, II, III, english edition. Translated and edited by Richard A. Silverman. Chelsea Publishing Co., New York (1977). [Google Scholar]
  27. J.M. Melenk, On Generalized Finite Element Methods. Ph.D. thesis. University of Maryland (1995). [Google Scholar]
  28. A.I. Markushevich, Operator adapted spectral element methods I: harmonic and generalized harmonic polynomials. Numer. Math. 84 (1999) 35–69. [CrossRef] [MathSciNet] [Google Scholar]
  29. J. M. Melenk and I. Babuška, The partition of unity finite element method: basic theory and applications. Comput. Methods Appl. Mech. Engrg. 139 (1996) 289–314. [Google Scholar]
  30. A. Moiola, Trefftz-discontinuous Galerkin methods for time-harmonic wave problems, Ph.D. thesis, Seminar for applied mathematics. ETH Zürich (2011). Available at: [Google Scholar]
  31. A. Moiola, R. Hiptmair and I. Perugia, Vekua theory for the Helmholtz operator. Z. Angew. Math. Phys. 62 (2011) 779–807. [CrossRef] [MathSciNet] [Google Scholar]
  32. P. Monk and D.Q. Wang, A least squares method for the Helmholtz equation. Comput. Methods Appl. Mech. Engrg. 175 (1999) 121–136. [Google Scholar]
  33. R. Nevanlinna and V. Paatero, Introduction to complex analysis. Translated from the German by T. Kövari and G.S. Goodman. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. (1969). [Google Scholar]
  34. 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 (2000). [CrossRef] [Google Scholar]
  35. C. Schwab, p- and hp-Finite Element Methods. Theory and Applications in Solid and Fluid Mechanics. Numerical Mathematics and Scientific Computation. Clarendon Press, Oxford (1998). [Google Scholar]
  36. I.N. Vekua, New methods for solving elliptic equations. North Holland (1967). [Google Scholar]
  37. J.L. Walsh, Interpolation and approximation by rational functions in the complex domain, 5th edition, vol. XX of American Mathematical Society Colloquium Publications. American Mathematical Society, Providence, R.I. (1969). [Google Scholar]
  38. R. Webster, Convexity, Oxford Science Publications. Oxford University Press, New York (1994). [Google Scholar]
  39. T.P. Wihler, Discontinuous Galerkin FEM for Elliptic Problems in Polygonal Domains. Ph.D. thesis, Swiss Federal Institute of Technology Zurich (2002). Available at: [Google Scholar]
  40. T.P. Wihler, P. Frauenfelder and C. Schwab, Exponential convergence of the hp-DGFEM for diffusion problems. p-FEM2000: p and hp finite element methods–mathematics and engineering practice (St. Louis, MO). Comput. Math. Appl. 46 (2003) 183–205. [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