Adaptive energy minimisation for hp-finite element methods. (February 2016)

• Record Type: Journal Article
• Authors: Houston, Paul; Wihler, Thomas P.
• Is Part Of: Computers & mathematics with applications. Volume 71:issue 4(2016)
• Page Start: 977
• Page End: 990
• Publication Date: 2016-02
• Subjects: Convex variational problems -- hp-finite element methods -- hp-adaptivity -- Quasilinear partial differential equations; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.01.002
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in an adaptive manner. Specifically, we outline a new approach in the context of h p -adaptive finite element methods employed for the efficient numerical solution of linear and nonlinear second-order boundary value problems. Numerical experiments are presented which highlight the practical performance of this new h p -refinement technique for both one- and two-dimensional problems.