AN A PRIORI ERROR ANALYSIS OF A STRAIN GRADIENT MODEL USING <i>C</i><sup>0</sup> INTERIOR PENALTY METHODS

Jacobo Baldonedo; José R. Fernández

doi:10.11948/20200374

2021 Volume 11 Issue 5

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Jacobo Baldonedo, José R. Fernández. AN A PRIORI ERROR ANALYSIS OF A STRAIN GRADIENT MODEL USING C0 INTERIOR PENALTY METHODS[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2303-2312. doi: 10.11948/20200374

Citation:

Jacobo Baldonedo, José R. Fernández. AN A PRIORI ERROR ANALYSIS OF A STRAIN GRADIENT MODEL USING C⁰ INTERIOR PENALTY METHODS[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2303-2312. doi: 10.11948/20200374

AN A PRIORI ERROR ANALYSIS OF A STRAIN GRADIENT MODEL USING C⁰ INTERIOR PENALTY METHODS

Jacobo Baldonedo¹,
José R. Fernández^2, ,

1.
CINTECX, Departamento de Ingeniería Mecánica, Universidade de Vigo, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
2.
Departamento de Matemática Aplicada I, Universidade de Vigo, Escola de Enxeñería de Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain

Corresponding author: Email: jose.fernandez@uvigo.es (J. R. Fernández)

Abstract

Abstract

In this work we study, from the numerical point of view, a strain gradient model. It can be written as a linear fourth-order in space and second-order in time partial differential equation which leads to a parabolic variational equation in terms of the velocity field. Then, a fully discrete approximation is provided by using the implicit Euler scheme to discretize the time derivatives and the so-called $ C^0 $ interior penalty method for the spatial approximation. A priori error estimates are obtained, and from them it follows the convergence of the approximations (under suitable regularity conditions). Finally, some two-dimensional numerical simulations are shown to demonstrate the numerical behaviour.
- Strain gradient theory /
- finite elements /
- C⁰ interior penalty methods /
- a priori error estimates /
- numerical simulations
MSC: 65M60, 65M12

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References

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