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

Friday, July 16, 15:30 ~ 16:00 UTC-3

On high-order conservative finite element methods for heterogeneous problems

Juan Galvis

Universidad Nacional de Colombia, Colombia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We describe and analyze a volumetric and residual-based Lagrange multipliers saddle point reformulation of the standard high-order finite method, to impose conservation of mass constraints for simulating the pressure equation on two dimensional convex polygons, with sufficiently smooth solution and mobility phase. We establish high-order a priori error estimates with locally conservative fluxes and numerical results are presented that confirm the theoretical results. For the numerical test we consider Qr finite element for homogeneous problems and GMsFEM discretization for heterogeneous problems. This talk is based on the papers:1) Computers & Mathematics with Applications Volume 75, Issue 6, 15 2018, Pages 1852-1867, 2) Multiscale Model. Simul., 18(4), 1375–1408. 2020.

Joint work with Marcus Sarkis(Department of Mathematical Sciences, Worcester Polytechnic Institute Worcester) and Eduardo Abreu (University of Campinas, Department of Applied Mathematics).

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