Crank–Nicolson extrapolation and finite element method for the Oldroyd fluid with the midpoint rule

Guo, Yingwen; He, Ya‐Ling

doi:10.1016/j.cam.2022.114453

Cited by 2 publications

(1 citation statement)

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“…Early work on the model and its finite element approximations can be found in previous research [3,4]. For time discrete schemes, we refer to other works [5][6][7] and the references therein. In addition to these, there are works based on stability analysis of time discrete schemes [8,9], projection methods [10,11], stabilized methods [12], characteristics finite element method [13], penalty method [14], and two-grid method [15] that have been carried out for this model.…”

Section: Introductionmentioning

confidence: 99%

A discontinuous Galerkin finite element method for the Oldroyd model of order one

Ray,

Goswami,

Bajpai

2024

Math Methods in App Sciences

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In this work, we analyze a discontinuous Galerkin finite element method for the equations of motion that arise in the 2D Oldroyd model of order one. We investigate the existence and uniqueness of semidiscrete discontinuous solutions, as well as the consistency of the scheme. We derive new a priori and regularity results for the discrete solution and establish optimal error estimates in ‐norm in time and energy norm in space for the velocity and ‐norm in both time and space for the pressure. Uniform estimates are derived for sufficiently small data. We next apply the backward Euler method to the semidiscrete formulation and establish optimal fully discrete error estimates. At the end, we conduct numerical experiments to support our theoretical results and analyze the findings.

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