TY - JOUR
T1 - Uniform discrete Sobolev estimates of solutions to finite difference schemes for singular limits of nonlinear PDEs
AU - Even-Dar Mandel, Liat
AU - Schochet, Steven
N1 - Publisher Copyright:
© EDP Sciences, SMAI 2017.
PY - 2017/3/1
Y1 - 2017/3/1
N2 - Uniform discrete Sobolev space estimates are proven for a class of finite-difference schemes for singularly-perturbed hyperbolic-parabolic systems. The estimates obtained improve previous results even when the PDEs do not involve singular perturbations. These estimates are used in a companion paper to prove the convergence of solutions as the discretization parameter and/or the singular perturbation parameter tends to zero.
AB - Uniform discrete Sobolev space estimates are proven for a class of finite-difference schemes for singularly-perturbed hyperbolic-parabolic systems. The estimates obtained improve previous results even when the PDEs do not involve singular perturbations. These estimates are used in a companion paper to prove the convergence of solutions as the discretization parameter and/or the singular perturbation parameter tends to zero.
KW - Discrete Sobolev spaces
KW - Finite-difference methods
KW - Fully-discrete sharp Gårding inequality
KW - Singular limits
KW - Uniform estimates
UR - http://www.scopus.com/inward/record.url?scp=85015316602&partnerID=8YFLogxK
U2 - 10.1051/m2an/2016038
DO - 10.1051/m2an/2016038
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AN - SCOPUS:85015316602
SN - 2822-7840
VL - 51
SP - 727
EP - 757
JO - ESAIM: Mathematical Modelling and Numerical Analysis
JF - ESAIM: Mathematical Modelling and Numerical Analysis
IS - 2
ER -