An Analysis of Axial Couette Flow in Annular Region of Abruptly Stopped Pipes

Thirumaran, V.; Weliwita, J. A.; Ishak, Mss

doi:10.9734/psij/2018/40076

Cited by 3 publications

(3 citation statements)

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“…The main idea of the regularization problem is to approach the considered ill-posed problem by a family of well-posed problems depending on a (small) regularization parameter. As similar we consider the regularized problem associated to the ill-posed problem (2.1)-(2.2)-(2.3) with > 0  is the regularization parameter and  is the noisy level resulting from the measurements of the given data 0 1 , u u , with condition [24,25]…”

Section: Regularization Methods and Convergence Estimatesmentioning

confidence: 99%

“…We consider the suite of functions ( , ) n q   , for > 0  and 0 < <   defi ned by [23,24] 2 2 ( , ) = ,…”

Section: Regularization Methods and Convergence Estimatesmentioning

confidence: 99%

“…In the conventional Treff tz method, the numerical solution for the two-dimensional Laplace equation in doubly-connected planar domain is expressed by linear summation of the following bases [3,22,24].…”

Section: Collocation Methodsmentioning

confidence: 99%

See 2 more Smart Citations

A Regularized Trefftz Method for Solving an Inverse Problem for the Laplace Equation

Hadj¹,

Saker²

2022

J Biomed Res Environ Sci

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The present paper proposes a new regularised Trefftz method to recover the boundary value on a non-accessible boundary of an annulus from overdetermined data on the accessible boundary of that annulus. Considering that the available data have a Fourier expansion, we consider the Tikhonov damping factor in constructing our regularized scheme, which satisfies the boundary value problem. At the same time, the convergence estimates for the regularised solution will be established under an assumption for the exact solution. The finite term truncation of the series expansion allows us to match the boundary condition as accurately as desired. By the collocation method, we derive a system of linear equations that can be uniquely solved to obtain the coefficients and preset the regularisation parameter and the damping factor to ensure adequate stability. The numerical efficiency of the proposed method is investigated with a high truncation number in comparison with the modified collocation Trefftz method.

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Section: Regularization Methods and Convergence Estimatesmentioning

confidence: 99%

“…We consider the suite of functions ( , ) n q   , for > 0  and 0 < <   defi ned by [23,24] 2 2 ( , ) = ,…”

Section: Regularization Methods and Convergence Estimatesmentioning

confidence: 99%

See 1 more Smart Citation

A Regularized Trefftz Method for Solving an Inverse Problem for the Laplace Equation

Hadj¹,

Saker²

2022

J Biomed Res Environ Sci

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Flow in Open and Closed Rectangular Channels with Moving Walls

Maghrebi

Moghaddam

2022

Iran J Sci Technol Trans Civ Eng

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A regularized Trefftz method for solving an inverse problem for the Laplace equation

Hadj

Saker

2022

Preprint

View full text Add to dashboard Cite

The present paper proposes a new regularized Trefftz method to recover the boundary value on a non-accessible boundary of an annulus from over determined data on the accessible boundary of that annulus. Considering that the available data have a Fourier expansion, we consider the Tikhonov damping factor in constructing our regularized scheme, which satisfies the boundary value problem. At the same time, the convergence estimates for the regularized solution will be established under an assumption for the exact solution. The finite term truncation of the series expansion allows us to match the boundary condition as accurately as desired. By the collocation method, we derive a system of linear equations that can be uniquely solved to obtain the coefficients and preset the regularization parameter and the damping factor to ensure adequate stability. The numerical efficiency of the proposed method is investigated with a high truncation number in comparison with the modified collocation Trefftz method.

show abstract

An Analysis of Axial Couette Flow in Annular Region of Abruptly Stopped Pipes

Cited by 3 publications

References 0 publications

A Regularized Trefftz Method for Solving an Inverse Problem for the Laplace Equation

A Regularized Trefftz Method for Solving an Inverse Problem for the Laplace Equation

Flow in Open and Closed Rectangular Channels with Moving Walls

A regularized Trefftz method for solving an inverse problem for the Laplace equation

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