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math.NA2016★ 63 cited
A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson--Nernst--Planck systems
Hailiang Liu, Zhongming Wang
We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully di…
math.NA2016
An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations
Hailiang Liu, Zhongming Wang
We propose a high order discontinuous Galerkin (DG) method for solving nonlinear Fokker-Planck equations with a gradient flow structure. For some of these models it is known that t…