discontinuous Galerkin finite element method for Hamilton-Jacobi equations

by Chang-Qing Hu

Publisher: National Aeronautics and Space Administration, Langley Research Center, Publisher: National Technical Information Service, distributor in Hampton, Va, [Springfield, Va

Written in English
Published: Pages: 24 Downloads: 227
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Subjects:

  • Finite element method.,
  • Galerkin methods.,
  • Hamilton-Jacobi equations -- Numerical solutions.

Edition Notes

Other titlesICASE
StatementChangquing Hu, Chi-Wang Shu.
SeriesICASE report -- no. 98-2, NASA/CR -- 1998-206903, NASA contractor report -- NASA CR-1998-206903.
ContributionsShu, Chi-Wang., Institute for Computer Applications in Science and Engineering., Langley Research Center.
The Physical Object
Pagination24 p. :
Number of Pages24
ID Numbers
Open LibraryOL19754322M

Benton, Stanley H. , The Hamilton-Jacobi equation: a global approach / Stanley H. Benton, Jr Academic Press New York Wikipedia Citation Please see Wikipedia's template documentation for further citation fields that may be required. The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal­ lenges facing the field of computational fluid dynamics. In structural me­ chanics, the advantages of high-order finite element approximation are. The Idea. The nite-element discretization which we propose is motiv ated by the idea of local solutions: At x h 2 h the nite-element solution u h 2 V h takes the value u h (x h) of the exact viscosity solution u h 2 C 0 ;1 (! h (x h)) that solves a simpli ed Hamilton-Jacobi equation on! h (x h) subject to the boundary conditions u h j @! h (x. Finite Element Methods with Artificial Diffusion for Hamilton-Jacobi-Bellman Equations Max Jensen⁄, Iain Smears † July 2, Abstract In this short note we investigate the numerical performance of the method of artificial diffusion for second-order fully nonlinear Hamilton-Jacobi-Bellman equations. The method was proposed in (M. Jensen.

The main article for this category is Partial differential equation. Wikimedia Commons has media related to Partial differential equations. This category has the following 16 subcategories, out of 16 total. The following pages are in this category, out of approximately total. This list may not reflect recent changes (learn more). @article{osti_, title = {Level set methods for detonation shock dynamics using high-order finite elements}, author = {Dobrev, V. A. and Grogan, F. C. and Kolev, T. V. and Rieben, R and Tomov, V. Z.}, abstractNote = {Level set methods are a popular approach to modeling evolving interfaces. We present a level set ad- vection solver in two and three dimensions using the . tions are discretised using the interior penalty discontinuous Galerkin nite element method that is divergence free to machine precision. A slope limiter made speci cally for exactly divergence free (solenoidal) elds is presented and used to illustrated the di culties in obtaining convectively stable elds that are also exactly by: 3. Non-linear Petrov-Galerkin methods for reduced order hyperbolic equations and discontinuous finite element methods. Numerical results show the new nonlinear Petrov-Galerkin method is a promising approach for stablisation of reduced order modelling. Fast sweeping methods are efficient iterative numerical schemes originally designed for Cited by:

Selected publications Article. Jensen, Max, Majee, Ananta K, Prohl, Andreas and Schellnegger, Christian () Dynamic programming for finite ensembles of nanomagnetic particles. Journal of Scientific Computing, 80 (1). pp. ISSN Jensen, Max () L²(H¹γ) finite element convergence for degenerate isotropic Hamilton–Jacobi–Bellman equations. Finite element methods, while low order, naturally work on unstructured meshes, and can compute physics inside and around complex, moving boundaries. Discontinuous Galerkin methods, which use high order polynomials within mesh elements, are significantly more accurate, but suffer because the complexity of linking the influence of the elements. We propose several advances in the simulation of fluids for computer graphics. We concentrate on particle-in-cell methods and related sub-problems. We develop high-order accurate extensions to particle-in-cell methods demonstrated on a variety of equations, including constrained dynamics with implicit-explicit time integration. We track the liquid-air interface with an explicit mesh, Cited by: 1. Publications in Refereed Journals [47] Y. Liu, Y. Cheng, S. Chen and Y.-T. Zhang, Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations, Journal of Computational Physics, v, (), pp. doi: / arXiv: [46] R. Zhao, Y.-T. Zhang and S. Chen, Krylov .

discontinuous Galerkin finite element method for Hamilton-Jacobi equations by Chang-Qing Hu Download PDF EPUB FB2

A DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR HAMILTON-JACOBI EQUATIONS CHANGQING HU AND CHI-WANG SHU * Abstract. In this paper, we present a discontinuous Galerkin finite clement method for solving the nonlinear Hamilton-Jacobi equations.

This method is based on the Runge-Kutta discontinuous GalerkinFile Size: 1MB. In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton--Jacobi equations.

This method is based on the Runge--Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high-order accuracy with a Cited by: Unlike the discontinuous Galerkin method of [C.

Hu, C.-W. Shu, A discontinuous Galerkin finite element method for Hamilton–Jacobi equations, SIAM Journal on Scientific Computing 21 () –] which applies the discontinuous Galerkin framework on the conservation law system satisfied by the derivatives of the solution, the method in Cited by: In this paper, we present a discontinuous Galerkin discontinuous Galerkin finite element method for Hamilton-Jacobi equations book element method for solving the nonlinear Hamilton--Jacobi equations.

This method is based on the Runge- Cited by: This volume contains current progress of a new class of finite element method, the Discontinuous Galerkin Method (DGM), which has been under rapid developments recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simulation, turbomachinery, turbulent flows, materials processing, Magneto-hydro-dynamics, plasma.

In this paper, we improve upon the discontinuous Galerkin (DG) method for Hamilton–Jacobi (HJ) equation with convex Hamiltonians in and develop a new DG method for directly solving the general HJ equations.

The new method avoids the reconstruction of the solution across elements by utilizing the Roe speed at the cell by: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula­ tion, turbomachinery, turbulent flows, materials processing, MHD and.

In this paper, a central discontinuous Galerkin method is proposed to solve for the viscosity solutions of Hamilton-Jacobi equations. Central discontinuous Galerkin methods were originally introduced for hyperbolic conservation laws.

They combine the central scheme and the discontinuous Galerkin method and therefore carry many features of both by:   A Discontinuous Galerkin Method Applied to Nonlinear Parabolic Equations.- III Contributed Papers.- Parallel Iterative Discontinuous Galerkin Finite-Element Methods.- A Discontinuous Projection Algorithm for Hamilton Jacobi Equations.- Successes and Failures of Discontinuous Galerkin Methods in Viscoelastic Fluid Analysis/5(2).

A central discontinuous Galerkin method for Hamilton-Jacobi equations Fengyan Li 1 and Sergey Yakovlev 2 Abstract In this paper, a central discontinuous Galerkin method is proposed to solve for the vis-cosity solutions of Hamilton-Jacobi equations.

Central discontinuous Galerkin methods were originally introduced for hyperbolic conservation by: Hamilton–Jacobi equations. Viscosity solution. In this work, we propose a high resolution Alternating Evolution Discontinuous Galerkin TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws.

III. One- B. dimensional systems, Phys. 84 (1) () 90– A discontinuous Galerkin finite element method for Hamilton-Jacobi equations: under contract NAS The Discontinuous Galerkin method is somewhere between a finite element and a finite volume method and has many good features of both.

An important distinction between the DG method and the usual finite-element method is that in the DG method the resulting equations are local to the generating element. Hamilton-Jacobi-like equations. A Discontinuous Galerkin Method Applied to Nonlinear Parabolic Equations.- III Contributed Papers.- Parallel Iterative Discontinuous Galerkin Finite-Element Methods.- A Discontinuous Projection Algorithm for Hamilton Jacobi Equations.- Successes and Failures of Discontinuous Galerkin Methods in Viscoelastic Fluid Analysis.-Author: Bernardo Cockburn.

Discontinuous Galerkin Finite Element Approximation of Hamilton--Jacobi--Bellman Equations with Cordes Coefficients Article in SIAM Journal on Numerical Analysis 52(2). This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential.

DISCONTINUOUS GALERKIN FINITE ELEMENT APPROXIMATION OF HAMILTON{JACOBI{BELLMAN EQUATIONS WITH CORDES COEFFICIENTS IAIN SMEARS AND ENDRE SULI y Abstract. We propose an hp-version discontinuous Galerkin nite element method for fully nonlinear second-order elliptic Hamilton{Jacobi{Bellman equations with Cord File Size: KB.

An h-Adaptive Runge-Kutta Discontinuous Galerkin Method for Hamilton-Jacobi Equations Hongqiang Zhu1 and Jianxian Qiu2,∗ 1 School of Natural Science, Nanjing University of Posts and Telecommunications, NanjingJiangsu, China. 2 School of Mathematical Sciences, Xiamen University, XiamenFujian, by: 1.

Cheng and C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics, v (), pp J.

Shen, C.-W. Shu and M. Zhang, High resolution schemes for a hierarchical size-structured model, SIAM Journal on Numerical Analysis, v45 (), pp DG method: first idea Essential points: u is discontinuous between elements, more than one node is defined at the interfaces between elements → numerical fluxes (which enable the connection between elements and the control of stability) The shape functions of an element are non zero only on the support of this elementFile Size: KB.

Introduction: Hamilton{Jacobi{Bellman (HJB) equations. Analysis: Analysis of HJB equations with Cordes coe cients. Motivation of Cordes coe cients Existence, Uniqueness, Well-posedness 3. Numerical methods: High-order discontinuous Galerkin methods for HJB equations with Cordes coe cients.

Local-structure-preserving discontinuous Galerkin methods with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations Wei Guo1, Fengyan Li2 and Jianxian Qiu3 Abstract: In this paper, a family of high order numerical methods are designed to solve the Hamilton-Jacobi equation for the viscosity solution.

In particular, the methods. DISCONTINUOUS GALERKIN FINITE ELEMENT APPROXIMATION OF HAMILTON–JACOBI–BELLMAN EQUATIONS WITH CORDES COEFFICIENTS∗ IAIN SMEARS† AND ENDRE SULI¨ † Abstract. We propose an hp-version discontinuous Galerkin finite element method for fully nonlinear second-order elliptic Hamilton–Jacobi–Bellman.

Get this from a library. Discontinuous Galerkin Methods: Theory, Computation and Applications. [B Cockburn; George E Karniadakis; Chi-Wang Shu] -- This volume contains current progress of a new class of finite element method, the Discontinuous Galerkin Method (DGM), which has been under rapid developments recently and has found its use very.

the method and illustrate the potential of exponential convergence under hp -refinement for problems with discontinuous coefficients and nonsmooth solutions. Key words. discontinuous Galerkin, hp-DGFEM, Cord`es condition, non-divergence form, dis-continuous coefficients, partial differential equations, finite element methods.

Finite Difference and Discontinuous Galerkin Finite Element Methods for Fully Nonlinear "Finite Difference and Discontinuous Galerkin Finite Element Methods for Fully Nonlinear Second Order Partial Differential Equations. " PhD diss., University of Tennessee, 5 The Vanishing Moment Method for Hamilton-Jacobi-Bellman Equa.

We will cover finite element methods for ordinary differential equations and for elliptic, parabolic and hyperbolic partial differential equations. Algorithm development, analysis, and computer implementation issues will be addressed.

In particular, we will discuss in depth the discontinuous Galerkin finite element method. APMA This book discusses a family of computational methods, known as discontinuous Galerkin methods, for solving partial differential equations.

While these methods have been known since the early s, they have experienced an almost explosive growth interest during the last ten to fifteen years, leading both to substantial theoretical developments and the application of these.

Abstract. Nondivergence form elliptic equations with discontinuous coefficients do not generally possess a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods.

We propose a new /ip-version. SPACE-TIME DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR TWO-FLUID FLOWS PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus, prof.

Brinksma, volgens besluit van het College voor promoties in het openbaar te verdedigen op vrijdag 16 april om uur door. Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations.

by. The IMA Volumes in Mathematics and its Applications (Book ) Thanks for Sharing! You submitted the following rating and review. We'll publish them on our site once we've reviewed : $In numerical solution of differential equations, WENO (weighted essentially non-oscillatory) methods are classes of high-resolution are used in the numerical solution of hyperbolic partial differential equations.

These methods were developed from ENO methods (essentially non-oscillatory). The first WENO scheme is developed by Liu, Chan and Osher in Finite difference: Parabolic, Forward-time .Finally, the book explains how these results can be extended to other more sophisticated conforming and non-conforming finite element methods, in particular to quadratic finite elements, local discontinuous Galerkin methods and a version of the SIPG method adding penalization on the normal derivatives of the numerical solution at the grid : Springer New York.