论文标题
对于一般的第四阶问题，具有变化系数
Robust nonconforming virtual element methods for general fourth order problems with varying coefficients
论文作者
论文摘要
我们为一类不合格的虚拟元素方法提供了二维的一般第四阶部分微分方程。我们开发了一种通用方法来构建必要的投影操作员和虚拟元素空间。对于具有不同系数的一般线性第四阶问题提供了能量规范中的最佳误差估计。我们还讨论了第四阶扰动问题，并提出了一种新颖的不合格方案，该方案相对于扰动参数均匀收敛，而无需扩大空间。进行数值测试以验证理论结果。最后，我们简要讨论了如何将方法轻松应用于非线性第四阶问题。
We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element spaces. Optimal error estimates in the energy norm are provided for general linear fourth order problems with varying coefficients. We also discuss fourth order perturbation problems and present a novel nonconforming scheme which is uniformly convergent with respect to the perturbation parameter without requiring an enlargement of the space. Numerical tests are carried out to verify the theoretical results. We conclude with a brief discussion on how our approach can easily be applied to nonlinear fourth order problems.
