InterPore2021

A space-time multiscale mortar mixed finite element method for flow in porous media

2 Jun 2021, 19:05

15m

Oral Presentation (MS7) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes MS7

Speaker

Ivan Yotov (University of Pittsburgh)

Description

We develop a space-time mortar mixed finite element method for
parabolic problems modeling flow in porous media. The domain is
decomposed into union of subdomains with non-matching grids and
different time steps. The space-time variational formulation couples
mixed finite elements in space with discontinuous Galerkin in time.
Continuity of flux across space-time interfaces is imposed via
coarse-scale space-time mortar finite elements, resulting in correct
mass conservation. A priori error estimates for the spatial and
temporal error are established. A space-time non-overlapping domain
decomposition method is developed that reduced the global problem to a
space-time coarse-scale mortar interface problem. Each interface
iteration requires solving space-time subdomain problems, which is
done in parallel. The convergence of the interface iteration is
analyzed. Numerical results illustrate the theoretical results and the
flexibility of the method for modeling flow in heterogeneous porous
media with features localized in space and time.