We initiate the design and the analysis of stabilization-free Virtual Element Methods for the laplacian problem written in mixed form. A Virtual Element version of the lowest order Raviart-Thomas Finite Element is considered. To reduce the computational costs, a suitable projection on the gradients of harmonic polynomials is employed. A complete theoretical analysis of stability and convergence is developed in the case of quadrilateral meshes. Some numerical tests highlighting the actual behaviour of the scheme are also provided.

翻译：针对以混合形式表述的拉普拉斯问题，我们启动了无稳定化虚拟元方法的设计与分析。采用了一种最低阶Raviart-Thomas有限元的虚拟元版本。为降低计算成本，引入了调和多项式梯度上的合适投影。针对四边形网格情况，开展了完整的稳定性和收敛性理论分析。文中还提供了一些数值算例，以阐明该方法的实际表现。