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A new three-field formulation of the biharmonic problem and its finite element discretization. (English) Zbl 1365.65249

Authors’ abstract: This paper considers a new three-field fomulation 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 the paper uses the standard Lagrange finite element to discretize the solution but uses 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 the approach.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J40 Boundary value problems for higher-order elliptic equations
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