Uniformly Convergent Finite Volume Schemes for a Convection-Dominated Equation with Discontinuous Coefficients. Application to Blood Flow Problems.

A two dimensional convection-dominated elliptic problem with discontinuous coefficients is considered. The problem is discretized using an inverse-monotone finite volume method on piecewise uniform (Shiskin) meshes, condensed near the boundary and the interior layers. A first-order global pointwise convergence uniform with respect to the perturbation parameter is established. Numerical experiments that support the theoretical results are presented. An inverse-monotone collocated finite volume method is applied for the numerical approximation of the generalized Navier-Stokes problem modeling unsteady non-Newtonian blood flow. The consistent splitting method is applied for time discretization. A Carreau-Yasuda model is used to describe the shear-thinning behavior of blood.