Approximation of singularly perturbed elliptic equations with convective terms in the case of a flow impinging on an impermeable wall (Q1571292)

The author considers the Dirichlet problem for an elliptic equation with convective terms on a rectangle. The coefficients of the highest-order derivatives contain a parameter \(\epsilon\), which can have any value in the half-open interval (0,1]. When the parameter is zero, the elliptic equation reduces to a first-order convection equation. The coefficients of the first-order derivatives correspond to a flow impinging on an impermeable wall: the flow velocities that are normal and tangential to the wall vanish on the wall and on the normal to the wall at the stagnation point. As the parameter approaches zero, a boundary-layer flow develops in the neighborhoods of the wall segment on which the flow impinges and the segment through which it leaves the domain. A procedure that substantiates the method of special condensing grids is proposed for problems of this class. An \(\epsilon\)-uniformly convergent difference scheme is constructed.