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Stability analysis of several first order schemes for the Oldroyd model with smooth and nonsmooth initial data
Author(s) -
Zhang Tong,
Qian Yanxia
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22283
Subject(s) - mathematics , discretization , stability (learning theory) , scheme (mathematics) , finite element method , galerkin method , discontinuous galerkin method , temporal discretization , order (exchange) , mathematical analysis , computer science , physics , finance , machine learning , economics , thermodynamics
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. TheH 2 ‐stability results of the different numerical schemes are provided, where the first‐order implicit and semi‐implicit schemes are theH 2 ‐unconditional stable, the implicit/explicit scheme is theH 2 ‐almost unconditional stable, and the first order explicit scheme is theH 2 ‐conditional stable. Finally, some numerical investigations of theH 2 ‐stability results of the considered numerical schemes for the Oldroyd model are provided to verify the established theoretical findings.