论文标题
a $ c^{0} $非差异形式的平面斜衍生物问题的有限元近似
A $C^{0}$ finite element approximation of planar oblique derivative problems in non-divergence form
论文作者
论文摘要
本文提出了一种$ c^{0} $（非拉格朗日）的原始有限元近似，以非差异形式的线性椭圆方程式在平面，弯曲域中具有倾斜边界条件的非差异形式。作为[Calcolo，58（2022），第9号]的扩展，通过增强顶点的规律性来确定离散水平下倾斜边界条件的Miranda-Talenti估计值。因此，所提出的方案的强制性常数与PDE理论完全相同。通过仔细研究有限元空间的近似特性来确定准最佳订单误差估计。提供了数值实验来验证收敛理论并证明所提出方法的准确性和效率。
This paper proposes a $C^{0}$ (non-Lagrange) primal finite element approximation of the linear elliptic equations in non-divergence form with oblique boundary conditions in planar, curved domains. As an extension of [Calcolo, 58 (2022), No. 9], the Miranda-Talenti estimate for oblique boundary conditions at a discrete level is established by enhancing the regularity on the vertices. Consequently, the coercivity constant for the proposed scheme is exactly the same as that from PDE theory. The quasi-optimal order error estimates are established by carefully studying the approximation property of the finite element spaces. Numerical experiments are provided to verify the convergence theory and to demonstrate the accuracy and efficiency of the proposed methods.
