Finite volume methods for convection-diffusion problems. (English) Zbl 0847.65075

Cell-centered finite difference approximations for second-order convection-diffusion equations of divergence type are considered. Approximation of the convection term in such problems by central finite differences leads to schemes of second order, which are stable only for sufficiently small mesh size \(h\). Therefore a number of modified upwind finite difference strategies is proposed, that provide a second order of accuracy and that are unconditionally stable (i.e. not only for small \(h\)). Furthermore they satisfy the discrete maximum principle. The error estimates are performed in the discrete Sobolev spaces associated with the considered boundary value problem.


65N06 Finite difference methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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