کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6929818 867531 2016 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation
چکیده انگلیسی
The invariant preserving property is one of the guiding principles for numerical algorithms in solving wave equations, in order to minimize phase and amplitude errors after long time simulation. In this paper, we design, analyze and numerically validate a Hamiltonian preserving discontinuous Galerkin method for solving the Korteweg-de Vries (KdV) equation. For the generalized KdV equation, the semi-discrete formulation is shown to preserve both the first and the third conserved integrals, and approximately preserve the second conserved integral; for the linearized KdV equation, all the first three conserved integrals are preserved, and optimal error estimates are obtained for polynomials of even degree. The preservation properties are also maintained by the fully discrete DG scheme. Our numerical experiments demonstrate both high accuracy of convergence and preservation of all three conserved integrals for the generalized KdV equation. We also show that the shape of the solution, after long time simulation, is well preserved due to the Hamiltonian preserving property.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 321, 15 September 2016, Pages 776-796
نویسندگان
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