Hybrid mixed discontinuous Galerkin finite element method for incompressible miscible displacement problem

TL;DR

This paper introduces a hybrid mixed discontinuous Galerkin finite element method for incompressible miscible displacement problems, emphasizing reduced unknowns and improved stability.

Contribution

The paper develops a novel hybrid mixed discontinuous Galerkin method combining pressure, velocity, and concentration equations with enhanced efficiency and theoretical guarantees.

Findings

Less unknowns and sparser stencils compared to traditional methods

Proven stability and optimal error estimates

Ensures consistency and conservation in simulations

Abstract

A new hybrid mixed discontinuous Galerkin finite element (HMDGFE) method is constructed for incompressible miscible displacement problem. In this method, the hybrid mixed finite element (HMFE) procedure is considered to solve pressure and velocity equations, and a new hybrid mixed discontinuous Galerkin procedure is constructed to solve the concentration equation with upwind technique. Compared with other traditional discontinuous Galerkin methods, the new method can reach global systems with less unknowns and sparser stencils. The consistency and conservation of the method are analyzed, the stability and optimal error estimates are also derived by the new technique.