Numerische Mathematik

, Volume 122, Issue 4, pp 709–723

Finite element approximation for time-dependent diffusion with measure-valued source

  • Thomas I. Seidman
  • Matthias K. Gobbert
  • David W. Trott
  • Martin Kružík
Article

DOI: 10.1007/s00211-012-0474-8

Cite this article as:
Seidman, T.I., Gobbert, M.K., Trott, D.W. et al. Numer. Math. (2012) 122: 709. doi:10.1007/s00211-012-0474-8

Abstract

The convergence of finite element methods for elliptic and parabolic partial differential equations is well-established if source terms are sufficiently smooth. Noting that finite element computation is easily implemented even when the source terms are measure-valued—for instance, modeling point sources by Dirac delta distributions—we prove new convergence order results in two and three dimensions both for elliptic and for parabolic equations with measures as source terms. These analytical results are confirmed by numerical tests using COMSOL Multiphysics.

Mathematics Subject Classification (2000)

35K5765M1565M60

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Thomas I. Seidman
    • 1
  • Matthias K. Gobbert
    • 1
  • David W. Trott
    • 1
  • Martin Kružík
    • 2
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of Maryland, Baltimore CountyBaltimoreUSA
  2. 2.Institute of Information Theory and AutomationAcademy of Sciences of the Czech RepublicPraha 8Czech Republic
  3. 3.Faculty of Civil EngineeringCzech Technical UniversityPraha 6Czech Republic