Stability analysis of several first order schemes for the Oldroyd model with smooth and nonsmooth initial data. Issue 6 (20th May 2018)

• Record Type: Journal Article
• Authors: Zhang, Tong; Qian, Yanxia
• Is Part Of: Numerical methods for partial differential equations. Volume 34:Issue 6(2018)
• Page Start: 2180
• Page End: 2216
• Publication Date: 2018-05-20
• Subjects: fully discrete schemes -- mixed finite element method -- oldroyd model -- H2‐stability; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22283
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : In this article, we develop several first order fully discrete Galerkin finite element schemes for the Oldroyd model and establish the corresponding stability results for these numerical schemes with smooth and nonsmooth initial data. The stable mixed finite element method is used to the spatial discretization, and the temporal treatments of the spatial discrete Oldroyd model include the first order implicit, semi‐implicit, implicit/explicit, and explicit schemes. The H 2 ‐stability results of the different numerical schemes are provided, where the first‐order implicit and semi‐implicit schemes are the H 2 ‐unconditional stable, the implicit/explicit scheme is the H 2 ‐almost unconditional stable, and the first order explicit scheme is the H 2 ‐conditional stable. Finally, some numerical investigations of the H 2 ‐stability results of the considered numerical schemes for the Oldroyd model are provided to verify the established theoretical findings.