TY - JOUR
T1 - A maximum principle for beltrami color flow
AU - Dascal, Lorina
AU - Sochen, Nir A.
PY - 2005
Y1 - 2005
N2 - We study, in this work, the maximum principle for the Beltrami color flow and the stability of the flow's numerical approximation by finite difference schemes. We discuss, in the continuous case, the theoretical properties of this system and prove the maximum principle in the strong and the weak formulations. In the discrete case, all the second order explicit schemes that are currently used violate, in general, the maximum principle. For these schemes we give a theoretical stability proof, accompanied by several numerical examples.
AB - We study, in this work, the maximum principle for the Beltrami color flow and the stability of the flow's numerical approximation by finite difference schemes. We discuss, in the continuous case, the theoretical properties of this system and prove the maximum principle in the strong and the weak formulations. In the discrete case, all the second order explicit schemes that are currently used violate, in general, the maximum principle. For these schemes we give a theoretical stability proof, accompanied by several numerical examples.
KW - Beltrami framework
KW - Finite difference schemes
KW - Maximum principle
KW - Parabolic PDEs
UR - http://www.scopus.com/inward/record.url?scp=27844461953&partnerID=8YFLogxK
U2 - 10.1137/S0036139903430835
DO - 10.1137/S0036139903430835
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AN - SCOPUS:27844461953
SN - 0036-1399
VL - 65
SP - 1615
EP - 1632
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 5
ER -