We propose and analyze a pressure-stabilized projection Lagrange--Galerkin scheme for the transient Oseen problem. The proposed scheme inherits the following advantages from the projection Lagrange--Galerkin scheme. The first advantage is computational efficiency. The scheme decouples the computation of each component of the velocity and pressure. The other advantage is essential unconditional stability. Here we also use the equal-order approximation for the velocity and pressure, and add a symmetric pressure stabilization term. This enriched pressure space enables us to obtain accurate solutions for small viscosity. First, we show an error estimate for the velocity for small viscosity. Then we show convergence results for the pressure. Numerical examples of a test problem show higher accuracy of the proposed scheme for small viscosity.

翻译：我们提议并分析一个压力稳定投影 Lagrange-Galerkin 方案,用于解决瞬间奥西恩问题。 拟议的方案继承了预测Lagrange- Galerkin 方案的以下优势。 第一个优势是计算效率。 这个方案拆分了速度和压力的每个组成部分的计算。 另一个优势是无条件的绝对稳定性。 我们在这里还使用速度和压力的等阶近似值, 并添加一个对称压力稳定化术语。 这个浓缩的压力空间可以让我们获得小粘度的准确解决方案。 首先, 我们显示了小粘度速度的错误估计值。 然后我们展示了压力的趋同结果。 一个测试问题的数值示例显示了小粘度拟议方案的更准确性 。