کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8902168 1631958 2018 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Superconvergence of the local discontinuous Galerkin method for the sine-Gordon equation in one space dimension
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Superconvergence of the local discontinuous Galerkin method for the sine-Gordon equation in one space dimension
چکیده انگلیسی
In this paper, we present superconvergence results for the local discontinuous Galerkin (LDG) method for the sine-Gordon nonlinear hyperbolic equation in one space dimension. We identify a special numerical flux and a suitable projection of the initial conditions for the LDG scheme for which the L2-norm of the LDG solution and its spatial derivative are of order p+1, when piecewise polynomials of degree at most p are used. Our numerical experiments demonstrate optimal order of convergence. We further prove superconvergence toward particular projections of the exact solutions. More precisely, we prove that the LDG solution and its spatial derivative are O(hp+3∕2) super close to particular projections of the exact solutions, while computational results show higher O(hp+2) convergence rate. Our analysis is valid for arbitrary regular meshes and for Pp polynomials with arbitrary p≥1. Numerical experiments validating these theoretical results are presented.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 333, 1 May 2018, Pages 292-313
نویسندگان
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