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An entropy stable high-order discontinuous Galerkin method for cross-diffusion gradient flow systems. (arXiv:1810.03221v1 [math.NA])
来源于:arXiv
As an extension of our previous work in Sun et.al (2018) [41], we develop a
discontinuous Galerkin method for solving cross-diffusion systems with a formal
gradient flow structure. These systems are associated with non-increasing
entropy functionals. For a class of problems, the positivity (non-negativity)
of solutions is also expected, which is implied by the physical model and is
crucial to the entropy structure. The semi-discrete numerical scheme we propose
is entropy stable. Furthermore, the scheme is also compatible with the
positivity-preserving procedure in Zhang (2017) [42] in many scenarios. Hence
the resulting fully discrete scheme is able to produce non-negative solutions.
The method can be applied to both one-dimensional problems and two-dimensional
problems on Cartesian meshes. Numerical examples are given to examine the
performance of the method. 查看全文>>