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

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 s...

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Bibliographic Details
Published in:Journal of scientific computing 2018-04, Vol.75 (1), p.350-375
Main Authors: Dubuis, Samuel, Picasso, Marco
Format: Article
Language:English
Subjects:
Adaptive algorithms
Algorithms
Computational Mathematics and Numerical Analysis
Crank-Nicholson method
Error analysis
Estimates
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Numerical analysis
Partial differential equations
Theoretical
Time dependence
Transport equations
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Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-017-0537-1