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Title of article :
Convergence of a crystalline approximation for an area-preserving motion
Author/Authors :
Ushijima، نويسنده , , Takeo K. and Yazaki، نويسنده , , Shigetoshi، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2004
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Abstract :
We consider an approximation of area-preserving motion in the plane by a generalized crystalline motion. The area-preserving motion is described by a parabolic partial differential equation with a nonlocal term, while the crystalline motion is governed by a system of ordinary differential equations. We show the convergence between these two motions. The convergence theorem is proved in two steps: first, an a priori estimate is established for a solution to the generalized crystalline motion; second, a discrete W1,p norms of the error is estimated for all 1⩽p<∞ and, passing p to infinity, a discrete W1,∞ error estimate is obtained. We also construct an implicit scheme which enjoys several nice properties such as the area-preserving and curve-shortening, and compare our scheme with a simple scheme.
Keywords :
Crystalline approximation , Crystalline motion , Crystalline curvature , A priori estimate , Convergence , Semi-discrete problem , Discrete W1 , p norm , Crystalline algorithm , Area-preserving , Discrete version of Wirtingerיs inequality , Curve-shortening
Journal title :
Journal of Computational and Applied Mathematics
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Link To Document :