论文标题
混合$ hp $ fem用于与两个小参数的单一扰动的第四阶边界价值问题
Mixed $hp$ FEM for singularly perturbed fourth order boundary value problems with two small parameters
论文作者
论文摘要
我们考虑了两个小参数的第四阶单一扰动的边界价值问题，以及通过\ cite {mxo}的{\ emph {peftral边界层}}网格上的有限元方法的$ hp $版本对解决方案的近似。我们使用的混合配方仅需要$ c^{0} $基础功能在二维平滑域中。在分析数据的假设下，我们表明该方法相对于两个奇异扰动参数均匀收敛，当时在能量规范中测量误差时，该方法以指数率的速率收敛。我们的理论发现是通过数值示例来说明的，包括使用更强（平衡）规范的结果。
We consider fourth order singularly perturbed boundary value problems with two small parameters, and the approximation of their solution by the $hp$ version of the Finite Element Method on the {\emph{Spectral Boundary Layer}} mesh from \cite{MXO}. We use a mixed formulation requiring only $C^{0}$ basis functions in two-dimensional smooth domains. Under the assumption of analytic data, we show that the method converges uniformly, with respect to both singular perturbation parameters, at an exponential rate when the error is measured in the energy norm. Our theoretical findings are illustrated through numerical examples, including results using a stronger (balanced) norm.
