On the convergence of spectral approximations for the heat convection equations

Climent-Ezquerra, Blanca; Poblete-Cantellano, Mariano; Rojas-Medar, Marko Antonio

doi:10.1007/s13163-016-0189-y

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2022

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“…Making use of this result, Rautmann ([18], [19]) proved the convergence rate in the ∥ • ∥ H 2 (Ω) -norm of the spectral Galerkin approximation of the solution without any compatibility condition. These results were extended to the finite element discretization of the Navier-Stokes equations by Bause [1], and to other systems of fluid mechanics by Boldrini et al (see [3]), and Climent-Ezquerra et al (see [6]).…”

Section: Introductionmentioning

confidence: 89%

On the convergence rate of Galerkin approximations for the magnetohydrodynamic type equations

Rodríguez-Bellido¹,

Rojas-Medar²,

Cerda³

2022

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The motion of incompressible electrical conducting fluids can be modeled by magnetohydrodynamics equations, which consider the Navier-Stokes equations coupled with Maxwell's equations. For the classical Navier-Stokes system, there exists an extensively study of the convergence rate for the Galerkin approximations. In this work, we extend the estimates rates of spectral Galerkin approximations for Navier-Stokes equations to the magnetohydrodynamic equations. We prove optimal error estimates in the L 2 (Ω) and H 1 (Ω)-norms and obtain a result similar to that one of Rautmann for the H 2 (Ω)-norm for the Navier-Stokes case. In this sense, we reach basically the same level of knowledge as in the case of the classical Navier-Stokes.

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