Optimal Control of Interface Problems with hp-finite Elements. (3rd March 2016)

• Record Type: Journal Article
• Authors: Wachsmuth, D.; Wurst, J.-E.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 3(2016)
• Page Start: 363
• Page End: 390
• Publication Date: 2016-03-03
• Subjects: Elliptic regularity -- higher-order finite elements -- optimal control -- transmission problems; 49M05 -- 65N30 -- 35J25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1149014
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We investigate the optimal control of elliptic partial differential equations with jumping coefficients. As discretization, we use interface concentrated finite elements on subdomains with smooth data. In order to apply convergence results, we prove higher regularity of the optimal solution using the concept of quasi-monotone coefficients and a domain that is injective modulo polynomials of degree 1 at each vertex. Numerical results are presented for a semi-linear control problem with a non-local radiation operator, which models the production process of silicon carbide single crystals.