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Gao Liping1; Zhang Bo2
Source Publicationsciencechinamathematics
AbstractThis paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D Maxwell equations in a lossy medium with a perfectly electric conducting (PEC) boundary condition, employing the energy method. To this end, we first establish some new energy identities for the 2D Maxwell equations in a lossy medium with a PEC boundary condition. Then by making use of these energy identities, it is proved that the FDTD scheme and its time difference scheme are stable in the discrete L~2 and H~1 norms when the CFL condition is satisfied. It is shown further that the solution to both the FDTD scheme and its time difference scheme is second-order convergent in both space and time in the discrete L~2 and H~1 norms under a slightly stricter condition than the CFL condition. This means that the solution to the FDTD scheme is superconvergent. Numerical results are also provided to confirm the theoretical analysis.
Document Type期刊论文
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GB/T 7714
Gao Liping,Zhang Bo. stabilityandsuperconvergenceanalysisofthefdtdschemeforthe2dmaxwellequationsinalossymedium[J]. sciencechinamathematics,2011,54(12):2693.
APA Gao Liping,&Zhang Bo.(2011).stabilityandsuperconvergenceanalysisofthefdtdschemeforthe2dmaxwellequationsinalossymedium.sciencechinamathematics,54(12),2693.
MLA Gao Liping,et al."stabilityandsuperconvergenceanalysisofthefdtdschemeforthe2dmaxwellequationsinalossymedium".sciencechinamathematics 54.12(2011):2693.
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