Maicon R. Correa

Two Families of

We develop two families of mixed finite elements on quadrilateral meshes for approximating

H

({\mathbf u},p)

(div) Mixed Finite Elements on Quadrilaterals of Minimal Dimension

solving a second order elliptic equation in mixed form. Standard Raviart--Thomas (RT) and Brezzi--Douglas--Marini (BDM) elements are defined on rectangles and extended to quadrilaterals using the Piola transform, which are well-known to lose optimal approximation of

A semi-discrete central scheme for incompressible multiphase flow in porous media in several space dimensions

\nabla\cdot{\mathbf u}

A new sequential method for three-phase immiscible flow in poroelastic media

. Arnold--Boffi--Falk spaces rectify the problem by increasing the dimension of RT, so that approximation is maintained after Piola mapping. Our two families of finite elements are uniformly inf-sup stable, achieve optimal rates of convergence, and have minimal dimension. The elements for

Unconditionally stable mixed finite element methods for Darcy flow

{\mathbf u}

A unified mixed formulation naturally coupling Stokes and Darcy flows

are constructed from vector polynomials defined directly on the quadrilaterals, rather than being transformed from a reference rectangle by the Piola mapping, and then supplemented by two (one for the lowest order) basis functions that are Piola mapped. One family has full

A semi-discrete central scheme for scalar hyperbolic conservation laws with heterogeneous storage coefficient and its application to porous media flow

H(div)

A new locally conservative numerical method for two-phase flow in heterogeneous poroelastic media

-approximation (

New Locally Conservative Numerical Schemes for Hydrogeomechanical Couplings in Strongly Heterogeneous Presalt Reservoirs

{\mathbf u}