88
Views
0
CrossRef citations to date
0
Altmetric
Original Article

Analysis of a Quadratic Finite Element Method for Second-Order Linear Elliptic PDE, With Low Regularity Data

ORCID Icon, &
Pages 507-541 | Received 15 May 2019, Accepted 30 Aug 2019, Published online: 17 Sep 2019

References

  • Casado-Díaz, J., Chacón Rebollo, T., Girault, V., Gómez Mármol, M., Murat, F. (2006). Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in L1. Numer. Math. 105(3):337–374. DOI: 10.1007/s00211-006-0033-2.
  • Dal Maso, G., Murat, F., Orsina, L., Prignet, A. (1999). Renormalized solutions of elliptic equations with general measure data. Ann. Scuola Norm. Sup. Pisa. 28:741–808.
  • Bénilan, P., Boccardo, L., Gallouët, T., Gariepy, R., Pierre, M., Vázquez, J. L. (1995). An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa. 22:241–273.
  • Ciarlet, P. G. (1978). The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland.
  • Boccardo, L., Gallouët, T. (1989). Nonlinear elliptic and parabolic equations involving measure data. J. Funct. Anal. 87(1):149–169. DOI: 10.1016/0022-1236(89)90005-0.
  • Horwitz, A. (2001). A version of Simpson’s rule for multiple integrals. J. Computat. Appl. Math. 134(1–2):1–11. DOI: 10.1016/S0377-0427(00)00444-1.
  • Glowinski, R. (1984). Numerical Methods for Nonlinear Variational Problems. Heidelberg: Springer-Verlag Berlin Heidelberg.
  • Drăgănescu, A. A., Dupont, T. F., Scott, L. R. (2004). Failure of the discrete maximum principle for an elliptic fnite element problem. Math. Comp. 74(249):1–23. DOI: 10.1090/S0025-5718-04-01651-5.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.