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

Journal Article


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.

Authors


  •   Droniou, Jerome (external author)
  •   Ilyas, Muhammad (external author)
  •   Lamichhane, Bishnu (external author)
  •   Wheeler, Glen E.

Publication Date


  • 2019

Citation


  • Droniou, J., Ilyas, M., Lamichhane, B. P. & Wheeler, G. E. (2019). A mixed finite element method for a sixth-order elliptic problem. IMA Journal of Numerical Analysis, 39 (1), 374-397.

Scopus Eid


  • 2-s2.0-85063399409

Number Of Pages


  • 23

Start Page


  • 374

End Page


  • 397

Volume


  • 39

Issue


  • 1

Place Of Publication


  • United Kingdom

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.

Authors


  •   Droniou, Jerome (external author)
  •   Ilyas, Muhammad (external author)
  •   Lamichhane, Bishnu (external author)
  •   Wheeler, Glen E.

Publication Date


  • 2019

Citation


  • Droniou, J., Ilyas, M., Lamichhane, B. P. & Wheeler, G. E. (2019). A mixed finite element method for a sixth-order elliptic problem. IMA Journal of Numerical Analysis, 39 (1), 374-397.

Scopus Eid


  • 2-s2.0-85063399409

Number Of Pages


  • 23

Start Page


  • 374

End Page


  • 397

Volume


  • 39

Issue


  • 1

Place Of Publication


  • United Kingdom