Approximation of the Ventcel problem, first numerical results

Charles Pierre (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

Report on the numerical approximation of the Ventcel problem. The Ventcel problem is a 3D eigenvalue problem involving a surface differential operator on the domain boundary: the Laplace Beltrami operator. \\ We present in the first section the problem statement together with its finite element approximation, the code machinery used for its resolution is also presented here. The last section presents the obtained numerical results. These results are quite unexpected for us. Either super-converging for $P^1$ Lagrange finite elements or under converging for $P^2$ and $P^3$. The remaining sections 2 and 3 provide numerical results either for the classical Laplace or for the Laplace Beltrami operator numerical approximation. These examples being aimed to validate the code implementation.

Mots clés: Ventcel's boundary value problem; Laplace-Beltrami operator; surface finite element methods

Domaines: Analyse numérique [math.NA]

Charles Pierre. Approximation of the Ventcel problem, first numerical results. 2014. ⟨hal-00985720v1⟩