论文标题
弯曲边缘的混合虚拟元素方法在两个维度上
The Mixed Virtual Element Method on curved edges in two dimensions
论文作者
论文摘要
在这项工作中，我们提出了具有曲线边缘元素的双维计算网格的混合虚拟元素方法（VEM）的扩展。具有曲面几何特征的域的直线边缘（例如域边界的一部分或内部界面）的近似值可能会引入几何误差，从而降低了方案收敛的预期顺序。在目前的工作中，提出了合适的VEM近似空间，以始终如一地处理曲线几何物体，从而恢复最佳收敛速率。介绍了所得的数值方案及其理论分析和几个数值测试用例，以验证所提出的方法。
In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical feature, such as a portion of domain boundary or an internal interface, may introduce a geometrical error that degrades the expected order of convergence of the scheme. In the present work a suitable VEM approximation space is proposed to consistently handle curvilinear geometrical objects, thus recovering optimal convergence rates. The resulting numerical scheme is presented along with its theoretical analysis and several numerical test cases to validate the proposed approach.
