Convex ENO Schemes for Hamilton–Jacobi Equations |
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| Authors: | Chi-Tien Lin Xu-Dong Liu |
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| Affiliation: | (1) Department of Applied Mathematics, Providence University, Taichung, 43301, Taiwan, Republic of China;(2) Department of Mathematics, UCSB, Santa Barbara, CA, USA |
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| Abstract: | In one dimension, viscosity solutions of Hamilton–Jacobi (HJ) equations can be thought as primitives of entropy solutions
for conservation laws. Based on this idea, both theoretical and numerical concepts used for conservation laws can be passed
to HJ equations even in several dimensions. In this paper, we construct convex ENO (CENO) schemes for HJ equations. This construction
is a generalization from the work by Liu and Osher on CENO schemes for conservation laws. Several numerical experiments are
performed. L
1 and L
∞ error and convergence rate are calculated as well. |
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| Keywords: | Convex ENO schemes Hamilton– Jacobi equations conservation laws |
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