A mixed finite-element method for elliptic operators with Wentzell boundary condition. (29th October 2018)

• Record Type: Journal Article
• Authors: Bänsch, Eberhard; Gahn, Markus
• Is Part Of: IMA journal of numerical analysis. Volume 40:Number 1(2020)
• Page Start: 87
• Page End: 108
• Publication Date: 2018-10-29
• Subjects: mixed finite-element method -- bulk-surface elliptic equations -- error-estimates -- Wentzell boundary condition; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry068
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: In this paper we introduce and analyze a mixed finite-element approach for a coupled bulk-surface problem of second order with a Wentzell boundary condition. The problem is formulated on a domain with a curved smooth boundary. We introduce a mixed formulation that is equivalent to the usual weak formulation. Furthermore, optimal a priori error estimates between the exact solution and the finite-element approximation are derived. To this end, the curved domain is approximated by a polyhedral domain introducing an additional geometrical error that has to be bounded. A computational result confirms the theoretical findings.