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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Adaptive Numerical Methods for Hamilton-Jacobi Equations

Adaptive Numerical Methods for Hamilton-Jacobi Equations

Kim, Kwang Il
Ri, Kwan Hung
Ri, Song Il

Paperback

General Mathematics

ISBN10: 3639861523
ISBN13: 9783639861525
Publisher: Scholars' Press
Published: Mar 10 2025
Pages: 132
Weight: 0.41
Height: 0.31 Width: 6.00 Depth: 9.00
Language: English
In recent years, Hamilton-Jacobi equations have attracted a lot of attention due to the important role that they play in various fields of applications.In this book, we introduce recent developments in adaptive numerical methods for Hamilton-Jacobi equations.We construct convergent adaptive high order schemes for time dependent Hamilton-Jacobi equations and propose a general method of constructing convergent adapive high order schemes and discuss the question of its convergence.Then, we propose a method of constructing convergent adaptive high order schemes for Hamilton-Jacobi equations on triangular meshes. According to this methodology, we construct adaptive schemes of WENO type on triangular meshes.Finally, we develop WENO schemes by newly defining nonlinear weights during WENO reconstruction which are not only simpler but also have clearer meaning than previous ones. Based on the analysis of numerical properties of the improved WENO scheme, we propose an algorithm of constructing a convergent adaptive WENO scheme by adapting the proposed WENO scheme through a newly introduced singularity indicator.

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