A Discontinuous Galerkin Solver for Front Propagation
نویسندگان
چکیده
We propose a new discontinuous Galerkin method based on [Y. Cheng and C.-W. Shu, J. Comput. Phys., 223 (2007), pp. 398–415] to solve a class of Hamilton–Jacobi equations that arises from optimal control problems. These equations are connected to front propagation problems or minimal time problems with nonisotropic dynamics. Several numerical experiments show the relevance of our method, in particular, for front propagation.
منابع مشابه
Convergence of discontinuous Galerkin schemes for front propagation with obstacles
We study semi-Lagrangian discontinuous Galerkin (SLDG) and RungeKutta discontinuous Galerkin (RKDG) schemes for some front propagation problems in the presence of an obstacle term, modeled by a nonlinear Hamilton-Jacobi equation of the form min(ut+cux, u−g(x)) = 0, in one space dimension. New convergence results and error bounds are obtained for Lipschitz regular data. These “low regularity” as...
متن کاملAdaptive discontinuous evolution Galerkin method for dry atmospheric flow
We present a new adaptive genuinely multidimensional method within the framework of the discontinuous Galerkin method. The discontinuous evolution Galerkin (DEG) method couples a discontinuous Galerkin formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of...
متن کاملMid - Year Report Discontinuous Galerkin Euler Equation Solver
The focus of this effort is to produce a two dimensional inviscid, compressible flow solver using the Discontinuous Galerkin Finite Element approach. The Discontinuous Galerkin method seeks to project the exact solution onto a finite polynomial space while allowing for discontinuities at cell interfaces. This allows for the natural discontinuity capture that is required for a compressible flow ...
متن کاملA Hybridized Crouziex-Raviart Nonconforming Finite Element and Discontinuous Galerkin Method for a Two-Phase Flow in the Porous Media
In this study, we present a numerical solution for the two-phase incompressible flow in the porous media under isothermal condition using a hybrid of the linear lower-order nonconforming finite element and the interior penalty discontinuous Galerkin (DG) method. This hybridization is developed for the first time in the two-phase modeling and considered as the main novelty of this research.The p...
متن کاملA discontinuous Galerkin scheme for front propagation with obstacles
We are interested in front propagation problems in the presence of obstacles. We extend a previous work (Bokanowski, Cheng and Shu [6]), to propose a simple and direct discontinuous Galerkin (DG) method adapted to such front propagation problems. We follow the formulation of Bokanowski et al. [7], leading to a level set formulation driven by min(ut + H(x,∇u), u − g(x)) = 0, where g(x) is an obs...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Scientific Computing
دوره 33 شماره
صفحات -
تاریخ انتشار 2011