| Abstract: |
| This talk is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint.
The first problem we consider consists in establishing the convergence of the error of the numerical approximation of the solution of a biharmonic obstacle problem. The contents of this section are meant to generalise the approach originally proposed by Ciarlet \& Raviart, and then complemented by Ciarlet \& Glowinski.
The second problem we consider amounts to studying a two-dimensional variational problem for linearly elastic shallow shells subjected to remaining confined in a prescribed half-space and we show that if the middle surface of the linearly elastic shallow shell under consideration is flat, the symmetry constraint required for formulating the constrained mixed variational problem announced in the second part of the paper is not required, and the solution can thus be approximated by solely resorting to Courant triangles. |
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