A DIVERGENCE-CONFORMING DISCONTINUOUS GALERKIN FINITE ELEMENTS FOR STOKES PROBLEM WITH VARIABLE VISCOSITY

Abstract

The Stokes problem deals with understanding how fluids move and deform under the influence of applied forces, such as gravity or pressure. The Stokes problem, a fundamental challenge in fluid dynamics, where the viscosity of the fluid varies across the domain. We employ a divergence-conforming discontinuous Galerkin 􀀀 Hdiv − DG

finite element approach, which specifically ensure that the computed solution maintains the divergence-free property of the velocity field. The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.