In this paper, we introduce and analyze a mixed formulation for the Oseen eigenvalue problem by introducing the pseudostress tensor as a new unknown, allowing us to eliminate the fluid pressure. The well-posedness of the solution operator is established using a fixed-point argument. For the numerical analysis, we use the tensorial versions of Raviart-Thomas and Brezzi-Douglas-Marini elements to approximate the pseudostress, and piecewise polynomials for the velocity. Convergence and a priori error estimates are derived based on compact operator theory. We present a series of numerical tests in two and three dimensions to confirm the theoretical findings.

翻译：本文通过引入拟应力张量作为新未知量，从而消除流体压力，提出并分析了 Oseen 特征值问题的一种混合变分形式。利用不动点论证建立了解算子的适定性。在数值分析中，我们采用 Raviart-Thomas 和 Brezzi-Douglas-Marini 单元的张量形式逼近拟应力，并采用分片多项式逼近速度。基于紧算子理论推导了收敛性和先验误差估计。我们通过一系列二维和三维数值实验验证了理论结果。