# Numerical verification of solutions for variational inequalities of the second kind

C. S. Ryoo, M. T. Nakao

Research output: Contribution to journalArticle

### Abstract

The purpose of this paper is to present an approach to the numerical proof of existence of solutions for the problem of the flow of a viscous plastic fluid in a pipe. Using the finite element approximations and the explicit a priori error estimates for the problem of the flow of a viscous plastic fluid in a pipe, we present an effective verification procedure that, through numerical computation, generates a set which includes the exact solution. Further, a numerical example is presented.

Original language English 1371-1380 10 Computers and Mathematics with Applications 43 10-11 https://doi.org/10.1016/S0898-1221(02)00105-0 Published - 2002 May Yes

### Fingerprint

Numerical Verification
Variational Inequalities
Plastics
Pipe
Fluid
A Priori Error Estimates
Fluids
Finite Element Approximation
Numerical Computation
Existence of Solutions
Exact Solution
Numerical Examples

### Keywords

• Error estimates
• Finite element method
• Numerical verification method
• Variational inequalities of the second kind

### ASJC Scopus subject areas

• Applied Mathematics
• Computational Mathematics
• Modelling and Simulation

### Cite this

Numerical verification of solutions for variational inequalities of the second kind. / Ryoo, C. S.; Nakao, M. T.

In: Computers and Mathematics with Applications, Vol. 43, No. 10-11, 05.2002, p. 1371-1380.

Research output: Contribution to journalArticle

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abstract = "The purpose of this paper is to present an approach to the numerical proof of existence of solutions for the problem of the flow of a viscous plastic fluid in a pipe. Using the finite element approximations and the explicit a priori error estimates for the problem of the flow of a viscous plastic fluid in a pipe, we present an effective verification procedure that, through numerical computation, generates a set which includes the exact solution. Further, a numerical example is presented.",
keywords = "Error estimates, Finite element method, Numerical verification method, Variational inequalities of the second kind",
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language = "English",
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AU - Ryoo, C. S.

AU - Nakao, M. T.

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N2 - The purpose of this paper is to present an approach to the numerical proof of existence of solutions for the problem of the flow of a viscous plastic fluid in a pipe. Using the finite element approximations and the explicit a priori error estimates for the problem of the flow of a viscous plastic fluid in a pipe, we present an effective verification procedure that, through numerical computation, generates a set which includes the exact solution. Further, a numerical example is presented.

AB - The purpose of this paper is to present an approach to the numerical proof of existence of solutions for the problem of the flow of a viscous plastic fluid in a pipe. Using the finite element approximations and the explicit a priori error estimates for the problem of the flow of a viscous plastic fluid in a pipe, we present an effective verification procedure that, through numerical computation, generates a set which includes the exact solution. Further, a numerical example is presented.

KW - Error estimates

KW - Finite element method

KW - Numerical verification method

KW - Variational inequalities of the second kind

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