We present a stable finite element formulation for the shallow water equations using the finite increment calculus (FIC) procedure. This research is focused on the stability properties of the FIC technique and uses linear triangles for the spatial discretization with an equal order of interpolation for all the variables. The extension to higher order polynomial interpolation functions and different geometries is straightforward. The present FIC-FEM procedure is also able to introduce artificial viscosity for an adequate shock capturing. An implicit time integration has been used. Special attention has been payed to the dry domain in order to solve the moving boundaries with a fixed mesh eulerian approach. Three academic examples are included in order to test the capabilities of the FIC-FEM procedure: the global stabilization, the shock capturing technique and the dry-wet interface. An experimental benchmark tests the overall accuracy of the present formulation.

我们使用有限增量演算 (FIC) 程序为浅水方程提供了一个稳定的有限元公式。这项研究的重点是 FIC 技术的稳定性属性，并使用线性三角形进行空间离散化，所有变量的插值顺序相同。对高阶多项式插值函数和不同几何形状的扩展很简单。目前的 FIC-FEM 程序还能够引入人工粘度以进行足够的震动捕获。已使用隐式时间积分。特别注意了干域，以便用固定网格解决移动边界欧拉方法。包括三个学术示例以测试 FIC-FEM 程序的能力：全局稳定、冲击捕获技术和干湿界面。实验基准测试当前配方的整体准确性。