L1-type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton-Jacobi equations |
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Authors: | Samala Rathan |
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Institution: | Faculty of Mathematics, Department of Humanities and Sciences, Indian Institute of Petroleum and Energy, Visakhapatnam, India |
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Abstract: | This article presents an improved fifth-order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton-Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L1-norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one- and two-dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme. |
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Keywords: | finite difference Hamilton-Jacobi equations nonlinear weights smoothness indicators undivided differences WENO scheme |
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