LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Publisher: Elsevier
Languages: English
Types: Article
Subjects:

Classified by OpenAIRE into

ACM Ref: MathematicsofComputing_NUMERICALANALYSIS
A discontinuous Galerkin method, with hp-adaptivity based on the approximate solution of appropriate dual problems, is employed for highly-accurate eigenvalue \ud computations on a collection of benchmark examples. After demonstrating the effectivity \ud of our computed error estimates on a few well-studied examples, we present results for several examples in which the coefficients of the partial-differential operators are discontinuous. \ud The problems considered here are put forward as benchmarks upon which other adaptive \ud methods for computing eigenvalues may be tested, with results compared to our own.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] H. Ammari, Y. Capdeboscq, H. Kang, and A. Kozhemyak. Mathematical models and reconstruction methods in magneto-acoustic imaging. European J. Appl. Math., 20(3):303-317, 2009.
    • [2] H. Ammari, H. Kang, E. Kim, and H. Lee. Vibration testing for anomaly detection. Math. Methods Appl. Sci., 32(7):863-874, 2009.
    • [3] H. Ammari, H. Kang, and H. Lee. Asymptotic analysis of high-contrast phononic crystals and a criterion for the band-gap opening. Arch. Ration. Mech. Anal., 193(3):679-714, 2009.
    • [4] D. Arnold, F. Brezzi, B. Cockburn, and L. Marini. Unified analysis of discontinuous galerkin methods for elliptic problems. SIAM J. Numer. Anal., 24(3):1749-1779, 2001.
    • [5] L. Banjai, S. B¨orm, and S. Sauter. FEM for elliptic eigenvalue problems: how coarse can the coarsest mesh be chosen? An experimental study. Comput. Vis. Sci., 11(4-6):363-372, 2008.
    • [6] R. Bank, L. Grubiˇsi´c, and J. S. Ovall. A framework for robust eigenvalue and eigenvector error estimation and ritz value convergence enhancement. MPI-MSI Preprint 42, 2010.
    • [7] R. Becker and R. Rannacher. An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer., 10:1-102, 2001.
    • [32] A. Knyazev and O. Widlund. Lavrentiev regularization + Ritz approximation = uniform finite element error estimates for differential equations with rough coefficients. Math. Comp., 72(241):17-40 (electronic), 2003.
    • [33] T. Koprucki, R. Eymard, and J. Fuhrmann. Convergence of a finite volume scheme to the eigenvalues of a schroedinger operator. Technical report, WIAS Preprint No. 1260, 2007.
    • [34] M. G. Larson. A posteriori and a priori error analysis for finite element approximations of self-adjoint elliptic eigenvalue problems. SIAM J. Numer. Anal., 38(2):608-625 (electronic), 2000.
    • [35] A. Naga, Z. Zhang, and A. Zhou. Enhancing eigenvalue approximation by gradient recovery. SIAM J. Sci. Comput., 28(4):1289-1300 (electronic), 2006.
    • [36] I. Perugia and D. Scho¨tzau. The hp-local discontinuous Galerkin method for low-frequency timeharmonic Maxwell equations. Math. Comp., 72(243):1179-1214, 2003.
    • [37] M. R. Racheva and A. B. Andreev. Superconvergence postprocessing for eigenvalues. Comput. Methods Appl. Math., 2(2):171-185, 2002.
    • [38] E. Sa´nchez-Palencia. Asymptotic and spectral properties of a class of singular-stiff problems. J. Math. Pures Appl. (9), 71(5):379-406, 1992.
    • [39] S. Sauter. hp-finite elements for elliptic eigenvalue problems: error estimates which are explicit with respect to λ, h, and p. SIAM J. Numer. Anal., 48(1):95-108, 2010.
    • [40] D. Scho¨tzau and L. Zhu. A robust a-posteriori error estimator for discontinuous galerkin methods for convection-diffusion equations. Appl. Numer. Math., 59:2236-2255, 2009.
    • [41] P. Stollmann. Caught by disorder, volume 20 of Progress in Mathematical Physics. Birkh¨auser Boston Inc., Boston, MA, 2001. Bound states in random media.
    • [42] J. Xu and A. Zhou. A two-grid discretization scheme for eigenvalue problems. Math. of Comput., 70(233):17-25, 2001.
    • [43] L. Zhu, S. Giani, P. Houston, and D. Scho¨tzau. Energy norm a-posteriori error estimation for hp-adaptive discontinuous galerkin methods for eliptic problems in three dimensions. Math. Models Methods Appl. Sci., (to appear), 2011. School of Mathematical Sciences University of Nottingham , University Park, Nottingham, NG7 2RD, United Kingdom E-mail address: University of Zagreb, Department of Mathematics, Bijenicˇka 30, 10000 Zagreb, Croatia E-mail address: University of Kentucky, Department of Mathematics, Patterson Office Tower 761, Lexington, KY 40506-0027, USA E-mail address:
  • No related research data.
  • No similar publications.

Share - Bookmark

Funded by projects

Cite this article