A posterior error estimates for the nonlinear grating problem with transparent boundary condition |
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Authors: | Zhoufeng Wang Yunzhang Zhang |
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Institution: | 1. Department of Mathematics, Nanjing University, Jiangsu, People's Republic of China;2. School of Mathematics and Statistics, Henan University of Science and Technology, Henan, People's Republic of China |
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Abstract: | 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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Keywords: | Maxwell's equation transparent boundary condition a posterior error estimates adaptive algorithm diffractive optics |
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