Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems

@inproceedings{Liska2007EnforcingTD,
  title={Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems},
  author={Richard Liska and Mikhail J. Shashkov},
  year={2007}
}
The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems. The preservation of the qualitative characteristics, such as the maximum principle, in discrete model is one of the key requirements. It is well known that standard linear finite element solution does not satisfy maximum principle on general triangular meshes in 2D. In this paper we consider how to enforce discrete maximum principle for linear finite element solutions for the… CONTINUE READING
Highly Cited
This paper has 58 citations. REVIEW CITATIONS
36 Citations
30 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-10 of 36 extracted citations

59 Citations

0510'09'11'13'15'17
Citations per Year
Semantic Scholar estimates that this publication has 59 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-10 of 30 references

Maximum principle and uniform convergence for the finite element method , Comput . Method

  • P. A. Raviart
  • Numer . Math .
  • 2007

Ern , Discrete maximum principle for galerkin approximations of the laplace operator on arbitrary meshes

  • E. Burman, A.
  • J . Comput . Appl . Math .
  • 2006

The repair paradigm: New algorithms and applications to compressible flow

  • R. L. Loubere, M. Staley, B. Wendroff
  • J. Comput. Phys., 211(2)
  • 2006

Similar Papers

Loading similar papers…