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
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات محاسباتی
پیش نمایش صفحه اول مقاله
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 pâ¥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
Journal: Applied Numerical Mathematics - Volume 115, May 2017, Pages 160-179
نویسندگان
Mahboub Baccouch,