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A Finite Volume Method to Solve the Ill-Posed Elliptic Problems

Author

Listed:
  • Ying Sheng

    (Department of Mathematics, Northeastern University, Shenyang 110004, China)

  • Tie Zhang

    (State Key Laboratory of Synthetical Automation for Process Industries, Department of Mathematics, Northeastern University, Shenyang 110004, China)

Abstract

In this paper, we propose a finite volume element method of primal-dual type to solve the ill-posed elliptic problem, that is, the elliptic problem with lacking or overlapping boundary value condition. We first establish the primal-dual finite volume element scheme by introducing the Lagrange multiplier λ and prove the well-posedness of the discrete scheme. Then, the error estimations of the finite volume solution are derived under some proper norms including the H 1 -norm. Numerical experiments are provided to verify the effectiveness of the proposed finite volume element method at last.

Suggested Citation

  • Ying Sheng & Tie Zhang, 2022. "A Finite Volume Method to Solve the Ill-Posed Elliptic Problems," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4220-:d:970319
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