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

Ying Sheng () and Tie Zhang
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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

Mathematics, 2022, vol. 10, issue 22, 1-17

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.

Keywords: ill-posed elliptic problem; finite volume element method; primal-dual scheme; well-posedness of discrete scheme; error estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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