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Anisotropic finite elements and the Crank–Nicolson scheme are considered to solve the time dependent transport equation. Anisotropic a priori and a posteriori error estimates are derived. The sharpness of the error indicator is studied on non-adapted meshes and time steps. An adaptive algorithm in space and time is then designed to control the error at final time. Numerical results show the accuracy of the method.

An Adaptive Algorithm for the Time Dependent Transport Equation with Anisotropic Finite Elements and the Crank–Nicolson Scheme