Numerical treatment of contact problems with thermal effect

Ochał, Anna; Jureczka, Michal

doi:10.3934/dcdsb.2018027

Cited by 3 publications

(2 citation statements)

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“…Factors to be taken into account include the type of the contact process (static, quasi-static, or dynamic), constitutive relations of the deformable bodies, contact conditions of various application-specific forms. In certain applications, it is important to consider heating or thermo effects ( [18]), or piezoelectricity effects ( [25]). Since the contact process inevitably causes material wear or even damage, it is not surprising that the wear effect has been built into mathematical models for a variety of contact processes, cf.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of a contact problem with wear

Han

Jureczka

et al. 2020

Computers & Mathematics with Applications

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This paper represents a sequel to [13] where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact surface of the body caused by the friction. Some preliminary error analysis for a fully discrete approximation of the contact problem was provided in [13]. In this paper, we consider a more general fully discrete numerical scheme for the contact problem, derive optimal order error bounds and present computer simulation results showing that the numerical convergence orders match the theoretical predictions.Keywords. Quasistatic contact problem, variational inequality, numerical methods, optimal order error estimate.

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Section: Introductionmentioning

confidence: 99%

Numerical analysis of a contact problem with wear

Han

Jureczka

et al. 2020

Computers & Mathematics with Applications

Self Cite

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show abstract

“…The next step in dealing with these cases is usually presenting the discrete numerical scheme and estimation of finite element method error. There are some examples of scientific works that provide the error estimation for particular cases, see for example [8][9][10][11] and the reference therein.…”

Section: Introductionmentioning

confidence: 99%