کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4645256 1632200 2013 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Convergence of a semi-discretization scheme for the Hamilton–Jacobi equation: A new approach with the adjoint method
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات محاسباتی
پیش نمایش صفحه اول مقاله
Convergence of a semi-discretization scheme for the Hamilton–Jacobi equation: A new approach with the adjoint method
چکیده انگلیسی

We consider a numerical scheme for the one dimensional time dependent Hamilton–Jacobi equation in the periodic setting. This scheme consists in a semi-discretization using monotone approximations of the Hamiltonian in the spacial variable. From classical viscosity solution theory, these schemes are known to converge. In this paper we present a new approach to the study of the rate of convergence of the approximations based on the nonlinear adjoint method recently introduced by L.C. Evans. We estimate the rate of convergence for convex Hamiltonians and recover the O(h) convergence rate in terms of the L∞L∞ norm and O(h)O(h) in terms of the L1L1 norm, where h is the size of the spacial grid. We discuss also possible generalizations to higher dimensional problems and present several other additional estimates. The special case of quadratic Hamiltonians is considered in detail in the end of the paper.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 73, November 2013, Pages 2–15
نویسندگان
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