Numerical Analysis Seminar - Jaime Manriquez. Title: A hybridizable discontinuous Galerkin method for Stokes/Darcy coupling in dissimilar meshes

Abstract. Nowadays, the development of higher-order schemes and non-body-fitted methods has become of interest in the community of numerical methods for partial differential equations (PDEs). A popular high-order method is the Hybridizable Discontinuous Galerkin (HDG) method, which presents the flexibility of DG methods with respect to more general grids, but with the advantage of reducing the high global number of degrees of freedom when using high polynomial degrees via hybridization of the intra-element variables . Almost two decades ago, the Transfer Path Method (TPM), based on a Taylor expansion extending solutions from polygonal subdomains to smooth boundaries, was developed as an unfitted method for the handling of geometrical non-conformities by transferring boundary data through a line integral (the transfer path) between the exact boundary and the discretized one. Recently the TPM has been applied to the case where a domain is divided into separate physical subdomains with different governing equations where the non-conformity is present at the interface. 

In this talk, I will give a short overview of the HDG-TPM method followed by the results obtained for a Stokes/Darcy coupling with two subdomains discretized by non-contiguous meshes (i.e. a gap between the discretizations leaves an unmeshed region of the domain).

This is joint work with Isaac Bermúdez and Manuel Solano.