2024/09/25 by Felipe Lepe, Lepe, Felipe, Gonzalo Rivera +3 · 1 citation
Computer Science · Engineering · #Contact Mechanics and Variational Inequalities #Elasticity and Material Modeling #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2409.17314
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.