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arXiv · 1710.02663

A mixed finite element method for a sixth order elliptic problem

Jérôme Droniou·Muhammad Ilyas·Bishnu Lamichhane·Glen E. Wheeler
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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.

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Jérôme Droniou, Muhammad Ilyas, Bishnu Lamichhane, Glen E. Wheeler. 2017-11-15. A mixed finite element method for a sixth order elliptic problem. https://arxiv.org/abs/1710.02663

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