A posterior error estimates for the nonlinear grating problem with transparent boundary condition | Zendy

Wang Zhoufeng | Zendy; Zhang Yunzhang | Zendy

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A posterior error estimates for the nonlinear grating problem with transparent boundary condition

Author(s) -

Wang Zhoufeng,

Zhang Yunzhang

Publication year - 2015

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.21937

Subject(s) - truncation (statistics) , truncation error , mathematics , boundary value problem , mathematical analysis , finite element method , nonlinear system , discretization , boundary (topology) , physics , statistics , quantum mechanics , thermodynamics

The nonlinear grating problem is modeled by Maxwell's equations with transparent boundary conditions. The nonlocal boundary operators are truncated by taking sufficiently many terms in the corresponding expansions. A finite element method with the truncation operators is developed for solving the nonlinear grating problem. The two posterior error estimates are established. The a posterior error estimate consists of two parts: finite element discretization error and the truncation error of the nonlocal boundary operators. In particular, the truncation error caused by truncation operations is exponentially decayed when the parameter N is increased. Numerical experiment is included to illustrate the efficiency of the method. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1101–1118, 2015

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