Séance Séminaire

Séminaire ACSIOM

An arbitrary-order primal hybrid discretization method for isotropic diffusion problems on general meshes. Application to the Laplace and Stokes equations

We propose a primal hybrid method of arbitrary order to construct numerically approximate solutions to isotropic diffusion problems on a bounded connected domain using very general meshes. In the framework of a parent work of D. Di Pietro & A. Ern on a mixed hybrid method, we construct additional operators such as local discrete gradient which allow one to condense locally a saddle-point discrete problem into a coercive discrete problem. The new problem is a priori much easier to solve numerically. As an application, we first consider the Laplace equation as a starting point. From which, we focus on the Stokes equation where a special attention will be given to the well-posedness property. Finally, a convergence analysis is carried out and numerical tests of both equations are presented.