A mixed finite element method for a sixth-order elliptic problem. (5th December 2017)

• Record Type: Journal Article
• Authors: Droniou, Jérôme; Ilyas, Muhammad; Lamichhane, Bishnu P; Wheeler, Glen E
• Is Part Of: IMA journal of numerical analysis. Volume 39:Number 1(2019)
• Page Start: 374
• Page End: 397
• Publication Date: 2017-12-05
• Subjects: sixth-order problem -- higher-order partial differential equations -- biharmonic problem -- mixed finite elements -- error estimates; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drx066
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: We consider a saddle-point formulation for a sixth-order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciarlet–Raviart formulation for the biharmonic problem to formulate our saddle-point problem and the finite element method. The new formulation allows us to use the $H^1$ -conforming Lagrange finite element spaces to approximate the solution. We prove a priori error estimates for our approach. Numerical results are presented for linear and quadratic finite element methods.