High-Order ADI Schemes for Convection-Diffusion Equations with Mixed Derivative Terms

International audienceWe present new high-order Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with cross derivative terms. Our approach is based on the unconditionally stable ADI scheme proposed by Hundsdorfer (Appl Numer Math 42:213-233, 2002). Different numerical discretizations which lead to schemes which are fourth-order accurate in space and second-order accurate in time are discussed