2022
DOI: 10.48550/arxiv.2202.04396
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A Priori Error Estimates of a Discontinuous Galerkin Finite Element Method for the Kelvin-Voigt Viscoelastic Fluid Motion Equations

Abstract: This paper applies a discontinuous Galerkin finite element method to the Kelvin-Voigt viscoelastic fluid motion equations when the forcing function is in L ∞ (L 2 )-space. Optimal a priori error estimates in L ∞ (L 2 )norm for the velocity and in L ∞ (L 2 )-norm for the pressure approximations for the semi-discrete discontinuous Galerkin method are derived here. The main ingredients for establishing the error estimates are the standard elliptic duality argument and a modified version of the Sobolev-Stokes oper… Show more

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