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arXiv · 2305.00407

An optimal error estimate for a mixed finite element method for a biharmonic problem with clamped boundary conditions

Bishnu P Lamichhane
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Abstract

We consider a mixed finite element method for a biharmonic equation with clamped boundary conditions based on biorthogonal systems with weakly imposed Dirichlet boundary condition. We show that the weak imposition of the boundary condition arising from a natural minimisation formulation allows to get an optimal a priori error estimate for the finite element scheme improving the existing error estimate for such a formulation without weakly imposed Dirichlet boundary condition. We also briefly outline the algebraic formulation arising from the finite element method.

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Bishnu P Lamichhane. 2023-04-30. An optimal error estimate for a mixed finite element method for a biharmonic problem with clamped boundary conditions. https://arxiv.org/abs/2305.00407

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