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This paper is concerned with the optimized Schwarz waveform relaxation methodand Ventcel transmission conditions for the linear advection-diffusionequation. A mixed formulation is considered in which the flux variablerepresents both diffusive and advective flux, and Lagrange multipliers areintroduced on the interfaces between nonoverlapping subdomains to handletangential derivatives in the Ventcel conditions. A space-time interfaceproblem is formulated and is solved iteratively. Each iteration involves thesolution of time-dependent problems with Ventcel boundary conditions in thesubdomains. The subdomain problems are discretized in space by a mixed hybridfinite element method based on the lowest-order Raviart-Thomas space and intime by the backward Euler method. The proposed algorithm is fully implicit andenables different time steps in the subdomains. Numerical results withdiscontinuous coefficients and various Pecl\'et numbers validate the accuracyof the method with nonconforming time grids and confirm the improvedconvergence properties of Ventcel conditions over Robin conditions.

Optimized Ventcel-Schwarz waveform relaxation and mixed hybrid finite element method for transport problems