论文标题
残留类型的HDG方法的后验错误分析Neumann边界控制问题
Residual-type a posteriori error analysis of HDG methods for Neumann boundary control problems
论文作者
论文摘要
我们研究了通过诺伊曼类型边界条件起作用的双侧盒子约束，对双边框约束下的线性二次边界控制问题的后验误差分析。我们采用可杂交的不连续盖金方法作为离散技术，而通量变量，标量变量和边界痕量变量均由度k的多项式近似。至于控制变量，它是由变异离散概念离散化的。然后，引入了有效且可靠的后验误差估计器，我们证明误差估计器为误差提供了上限和下限。最后，提出了数值结果，以说明获得的后验误差估计器的性能。
We study a posteriori error analysis of linear-quadratic boundary control problems under bilateral box constraints on the control which acts through a Neumann type boundary condition. We adopt the hybridizable discontinuous Galerkin method as discretization technique, and the flux variables, the scalar variables and the boundary trace variables are all approximated by polynomials of degree k. As for the control variable, it is discretized by the variational discretization concept. Then an efficient and reliable a posteriori error estimator is introduced, and we prove that the error estimator provides an upper bound and a lower bound for the error. Finally, numerical results are presented to illustrate the performance of the obtained a posteriori error estimator.
