A Family of Fully Discrete Linearly Extrapolated Curvature Stabilized Method for the Diffusion‐Peterlin Viscoelastic Fluid Model

ABSTRACT This paper proposes a family of fully discrete, second‐order linearly extrapolated curvature‐stabilized ‐schemes for solving the diffusive Peterlin viscoelastic model. By varying , we obtain distinct second‐order temporal schemes: at , the algorithm reduces to the BDF2 extrapolation method, while yields the Crank‐Nicolson extrapolation. We rigorously establish the existence and uniqueness of the discrete solutions, along with optimal error estimates for both the velocity and the conformation tensor under suitable regularity assumptions. The analysis highlights the role of the stabilization in ensuring stability without compromising second‐order accuracy. Three numerical experiments validate the theoretical analysis, demonstrating the scheme's second‐order convergence, and effectiveness in simulating the diffusive Peterlin model.