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210708n^^^^^^^^xx^^^^^^s^^^^^^^^^^^eng^d |
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|a Dual-Wind Discontinuous Galerkin Methods for Stationary Hamilton-Jacobi Equations and Regularized Hamilton-Jacobi Equations |h [electronic resource]. |
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|a This paper develops and analyzes a new family of dual-wind discontinuous Galerkin (DG) methods for stationary Hamilton-Jacobi equations and their vanishing viscosity regularizations. The new DG methods are designed using the DG finite element discrete calculus framework of [17] that defines discrete differential operators to replace continuous differential operators when discretizing a partial differential equation (PDE). The proposed methods, which are non-monotone, utilize a dual-winding methodology and a new skew-symmetric DG derivative operator that, when combined, eliminate the need for choosing indeterminable penalty constants. The relationship between these new methods and the local DG methods proposed in [38] for Hamilton-Jacobi equations as well as the generalized-monotone finite difference methods proposed in [13] and corresponding DG methods proposed in [12] for fully nonlinear second order PDEs is also examined. Admissibility and stability are established for the proposed dual-wind DG methods. The stability results are shown to hold independent of the scaling of the stabilizer allowing for choices that go beyond the Godunov barrier for monotone schemes. Numerical experiments are provided to gauge the performance of the new methods. |
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|a Electronic reproduction. |c University of Curacao Institutional Repository, |c University of the Virgin Islands, |d 2021. |f (UVI Digital Library) |n Mode of access: World Wide Web. |n System requirements: Internet connectivity; Web browser software. |
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|a University of the Virgin Islands. |
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|a Collected for University of Curacao's Institutional Repository by the UFIR Self-Submittal tool. Submitted by Janice Simon. |
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|a Journal Article |2 sobekcm |
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|a UVI |c Faculty Publications |
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|u https://uvi.sobeklibrary.com/IR00000030/00001 |y Electronic Resource |
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|a https:/uvi.sobeklibrary.com/content/IR/00/00/00/30/00001/Rapp, Aaron 2021_Article_HJ DWDGthm.jpg |
