کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5776699 1632158 2017 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Superconvergence of the discontinuous Galerkin method for nonlinear second-order initial-value problems for ordinary differential equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات محاسباتی
پیش نمایش صفحه اول مقاله
Superconvergence of the discontinuous Galerkin method for nonlinear second-order initial-value problems for ordinary differential equations
چکیده انگلیسی
In this paper, we propose and analyze a superconvergent discontinuous Galerkin (DG) method for nonlinear second-order initial-value problems for ordinary differential equations. Optimal a priori error estimates for the solution and for the auxiliary variable that approximates the first-order derivative are derived in the L2-norm. The order of convergence is proved to be p+1, when piecewise polynomials of degree at most p are used. We further prove that the p-degree DG solutions are O(h2p+1) superconvergent at the downwind points. Finally, we prove that the DG solutions are superconvergent with order p+2 to a particular projection of the exact solutions. The proofs are valid for arbitrary nonuniform regular meshes and for piecewise Pp polynomials with arbitrary p≥1. Computational results indicate that the theoretical orders of convergence and superconvergence are optimal.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 115, May 2017, Pages 160-179
نویسندگان
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