A mixed finite element method for a sixth-order elliptic problem

Jérôme Droniou, Muhammad Ilyas, Bishnu P. Lamichhane, Glen E. Wheeler

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5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)374-397
Number of pages24
JournalIMA Journal of Numerical Analysis
Volume39
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Biharmonic problem
  • Error estimates
  • Higher-order partial differential equations
  • Mixed finite elements
  • Sixth-order problem

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