Nonlinear Galerkin Finite Element for Viscoelastic Fluid Flow: Optimal Error Estimate
This work provides a theoretical improvement in error analysis for numerical simulation of viscoelastic flows, relevant to computational fluid dynamics researchers.
The paper presents a nonlinear Galerkin finite element method for viscoelastic fluid flow (Oldroyd model) and achieves an optimal error estimate in the L∞(L2) norm, improving upon previous L2(H1) estimates.
In this article, we discuss a couple of nonlinear Galerkin method (NLG) in finite element set up for viscoelastic fluid flow, mainly equations of motion arising in the flow of 2D Oldroyd model. We obtain improved error estimate in $L^{\infty}(\bL^2)$ norm, which is optimal in nature, for linear finite element approximation, in view of the error estimate available in literature, in $L^2(\bH^1)$ norm.