TY - JOUR
T1 - Convergence of Numerical Schemes for a Conservation Equation with Convection and Degenerate Diffusion
AU - Eymard , R.
AU - Guichard , C.
AU - Lhébrard , Xavier
JO - Journal of Computational Mathematics
VL - 3
SP - 428
EP - 452
PY - 2021
DA - 2021/04
SN - 39
DO - http://doi.org/10.4208/jcm.2002-m2018-0287
UR - https://global-sci.org/intro/article_detail/jcm/18745.html
KW - Linear convection, Degenerate diffusion, Gradient discretisation method,
$θ$-scheme.
AB - <p style="text-align: justify;">The approximation of problems with linear convection and degenerate nonlinear diffusion, which arise in the framework of the transport of energy in porous media with
thermodynamic transitions, is done using a $θ$-scheme based on the centred gradient discretisation method. The convergence of the numerical scheme is proved, although the test
functions which can be chosen are restricted by the weak regularity hypotheses on the convection field, owing to the application of a discrete Gronwall lemma and a general result for
the time translate in the gradient discretisation setting. Some numerical examples, using
both the Control Volume Finite Element method and the Vertex Approximate Gradient
scheme, show the role of $θ$ for stabilising the scheme.</p>