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### Session S20 - Applied Math and Computational Methods and Analysis across the Americas

Friday, July 16, 12:30 ~ 13:00 UTC-3

## A priori error estimates for a linear coupled elliptic problem using a mixed Hybrid High Order method

### Rommel Bustinza

#### Universidad de Concepcion, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloaka103fdbab0d63e141084a24114e01bab').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addya103fdbab0d63e141084a24114e01bab = 'rb&#117;st&#105;nz' + '&#64;'; addya103fdbab0d63e141084a24114e01bab = addya103fdbab0d63e141084a24114e01bab + '&#105;ng-m&#97;t' + '&#46;' + '&#117;d&#101;c' + '&#46;' + 'cl'; var addy_texta103fdbab0d63e141084a24114e01bab = 'rb&#117;st&#105;nz' + '&#64;' + '&#105;ng-m&#97;t' + '&#46;' + '&#117;d&#101;c' + '&#46;' + 'cl';document.getElementById('cloaka103fdbab0d63e141084a24114e01bab').innerHTML += '<a ' + path + '\'' + prefix + ':' + addya103fdbab0d63e141084a24114e01bab + '\'>'+addy_texta103fdbab0d63e141084a24114e01bab+'<\/a>';

We analyze a linear coupled elliptic problem in a bounded domain, applying a mixed formulation of the Hybrid High Order (HHO) method. This approach gives approximation of the unknowns in the interior volume of each element and on the faces of its boundary, in the sense that the approximations of the exact solution are sought in the space of polynomials of total degree $k\,\geq\,0$ on the mesh elements and faces. Thus, we obtain a non-conforming discrete formulation, which is well posed, and after a condensation process, we can reduce it to another scheme defined on the skeleton induced by the mesh. This allows us to obtain a more compact system and reduce significantly the number of unknowns. We point out that we need to introduce an auxiliary unknown (Lagrange multiplier) in order to deal with the non homogeneous transmission / coupling conditions. We prove that the method is convergent in the energy norm, as well as in the $L^2-$norm for the potential, and a weighted $L^2-$norm for the Lagrange multiplier, for smooth enough exact solutions. Moreover, we can establish a kind of a super convergence result of an approximation of the potential, obtained by a post process. Finally, we include some numerical experiments that validate our theoretical results, even in situations not fully covered by the current analysis

Joint work with Jonathan Munguia (Universidad Nacional de Ingeniería, Perú).