Journal of Computational Physics
SIAM Journal on Numerical Analysis
Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms
Applied Numerical Mathematics
Contractivity of domain decomposition splitting methods for nonlinear parabolic problems
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
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We propose and analyze an efficient numerical method for solving semilinear parabolic problems with mixed derivative terms on non-rectangular domains. The spatial semidiscretization process is based on an expanded mixed finite element scheme which, combined with suitable quadrature rules, is converted into a cell-centered finite difference scheme. This choice preserves the asymptotic accuracy and local conservation of mass of the method, while substantially reducing the computational cost of the totally discrete scheme. To obtain it, an alternating direction implicit scheme is used for the integration in time. The resulting numerical algorithm involves sets of uncoupled tridiagonal systems which can be solved in parallel. We set out some theoretical results of unconditional convergence (of second order in space and first order in time) for our method. Finally, a numerical experiment is shown in order to illustrate the theoretical results.