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

Title: A mixed finite element method for a sixth-order elliptic problem
Creator: Droniou, Jérôme; Ilyas, Muhammad; Lamichhane, Bishnu P.; Wheeler, Glen E.
Relation: IMA Journal of Numerical Analysis Vol. 39, Issue 1, p. 374-397
Publisher Link: http://dx.doi.org/10.1093/imanum/drx066
Publisher: Oxford University Press
Resource Type: journal article
Date: 2019
Description: 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 H1-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.
Subject: sixth-order problem; higher-order partial differential equations; biharmonic problem; mixed finite elements; error estimates
Identifier: http://hdl.handle.net/1959.13/1443486
Identifier: uon:42010
Identifier: ISSN:0272-4979
Language: eng
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