A Non-standard Finite Element Method Based on Boundary Integral Operators

  • Clemens Hofreither
  • Ulrich Langer
  • Clemens Pechstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)


This paper provides an overview over our results on the construction and analysis of a non-standard finite element method that is based on the use of boundary integral operators for constructing the element stiffness matrices. This approach permits polyhedral element shapes as well as meshes with hanging nodes. We consider the diffusion equation and convection-diffusion-reaction problems as our model problems, but the method can also be generalized to more general problems like systems of partial differential equations. We provide a rigorous H 1- and L 2-error analysis of the method for smooth and non-smooth solutions. This a priori discretization error analysis is only done for the diffusion equation. However, our numerical results also show good performance of our method for convection-dominated diffusion problems.


non-standard FEM boundary integral operators Trefftz method polyhedral meshes convection-diffusion-reaction problems 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Clemens Hofreither
    • 1
  • Ulrich Langer
    • 2
  • Clemens Pechstein
    • 2
  1. 1.DK Computational MathematicsJohannes Kepler University LinzLinzAustria
  2. 2.Institute of Computational MathematicsJohannes Kepler University LinzLinzAustria

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