Convergent semidiscretization of a nonlinear fourth order parabolic system
Convergent semidiscretization of a nonlinear fourth order parabolic system
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DOI：
10.1051/m2an:2003026
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发表时间：
2003-03
期刊：
影响因子：
--
通讯作者：
A. Jüngel;R. Pinnau
中科院分区：
文献类型：
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作者：
A. Jüngel;R. Pinnau
研究了量子半导体模型中四阶非线性抛物系统在时间上的半离散化问题。通过引入附加的非线性势能对系统进行了数值处理。利用离散化的稳定性，在多维情形下证明了算法的收敛特性。在对解的正则性作一定的假设下，证明了收敛速度是最优的。
A semidiscretization in time of a fourth order nonlinear parabolic system in several space dimensions arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an additional nonlinear potential. Exploiting the stability of the discretization, convergence is shown in the multi-dimensional case. Under some assumptions on the regularity of the solution, the rate of convergence proves to be optimal.