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A new three‐field formulation of the biharmonic problem and its finite element discretization
Author(s) -
Banz Lothar,
Lamichhane Bishnu P.,
Stephan Ernst P.
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22082
Subject(s) - biharmonic equation , lagrange multiplier , discretization , mathematics , finite element method , partial differential equation , lagrange polynomial , mixed finite element method , mathematical analysis , mathematical optimization , boundary value problem , physics , polynomial , thermodynamics
We consider a new three‐field formulation of the biharmonic problem. The solution, the gradient and the Lagrange multiplier are the three unknowns in the formulation. Adding a stabilization term in the discrete setting we can use the standard Lagrange finite element to discretize the solution, whereas we use the Raviart‐Thomas finite element to discretize the gradient. The Lagrange multipliers are constructed to achieve the optimal error estimate. Numerical results are presented to demonstrate the performance of our approach. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 199–217, 2017