TY - JOUR
T1 - Nonnegativity-Preserving Repair Techniques for the Finite Element Solutions of Degenerate Nonlinear Parabolic Problems
AU - Junliang Lv, Guangwei Yuan & Jingyan Yue
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 413
EP - 436
PY - 2018
DA - 2018/11
SN - 11
DO - http://doi.org/10.4208/nmtma.2017-OA-0125
UR - https://global-sci.org/intro/article_detail/nmtma/12437.html
KW - 
AB - <p style="text-align: justify;">In the numerical simulation for nonlinear diffusion problems with degenerate diffusion coefficients,
some classical methods are often invalid since they involve
a harmonic mean of diffusion coefficients on the adjacent cells. To avoid such problem,
we consider using linear finite element method to solve a class of 1D degenerate nonlinear parabolic equations.
This method can effectively capture the profile of true solution, but at the front it generates
some nonphysical numerical oscillations, even brings forth negative values in numerical solution
for approximating nonnegative physical quantities. In order to preserve the nonnegativity of true solution,
we discuss three repair techniques for finite element solutions based on a posteriori corrections.
The first one is a zero-setting method, in which we directly set those negative values to be zero.
The second one is a local approach, in which any negative energy associate to some node
is absorbed by the positive values around the current node. The third one is a global strategy,
in which the total negative energy is redistributed to all positive values with a one-time effort.
Numerical examples show that the numerical solution profile is improved remarkably by using the repair techniques
for degenerate parabolic equations.</p>