Coupling regularization and adaptive hp-BEM for the solution of a delamination problem

Ovcharova, Nina; Banz, Lothar

doi:10.1007/s00211-017-0879-5

Cited by 15 publications

(4 citation statements)

References 37 publications

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“…For a deeper study that relates the conditions ( 10) and ( 11) to the jumps of ∂j we can refer to [40].…”

Section: Some Preliminaries and The Interface Problemmentioning

confidence: 99%

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Coupling of finite element and boundary element methods with regularization for a nonlinear interface problem with nonmonotone set-valued transmission conditions

Gwinner¹,

Ovcharova²

2021

Preprint

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For the first time, a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions is analyzed. The investigated problem involves a nonlinear monotone partial differential equation in the interior domain and the Laplacian in the exterior domain. Such a scalar interface problem models nonmonotone frictional contact of elastic infinite media. The variational formulation of the interface problem leads to a hemivariational inequality, which lives on the unbounded domain, and so cannot be treated numerically in a direct way. By boundary integral methods the problem is transformed and a novel hemivariational inequality (HVI) is obtained that lives on the interior domain and on the coupling boundary, only. Thus for discretization the coupling of finite elements and boundary elements is the method of choice. In addition smoothing techniques of nondifferentiable optimization are adapted and the nonsmooth part in the HVI is regularized. Thus we reduce the original variational problem to a finite dimensional problem that can be solved by standard optimization tools. We establish not only convergence results for the total approximation procedure, but also an asymptotic error estimate for the regularized HVI.

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“…For a deeper study that relates the conditions ( 10) and ( 11) to the jumps of ∂j we can refer to [40].…”

Section: Some Preliminaries and The Interface Problemmentioning

confidence: 99%

“…The errror analysis in this paper has focused to the classical h-method of BEM/FEM discretization, for the more versatile hp-BEM and hp-FEM applied to unilateral contact problems, albeit in bounded domains, we refer to [40] and to [23], respectively.…”

Section: Conclusion and An Outlookmentioning

confidence: 99%

Coupling of finite element and boundary element methods with regularization for a nonlinear interface problem with nonmonotone set-valued transmission conditions

Gwinner¹,

Ovcharova²

2021

Preprint

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“…We refer to the book [5] where the existence, uniqueness, and convergence results for various class of variational-hemivariational inequalities were studied, as well as the applications of these inequalities in the study of mathematical models which describe the contact between a deformable body and a foundation. Recently, semicoercive variational-hemivariational inequalities were studied via regularization techniques, and used to model unilateral contact problems with nonmonotone boundary conditions as well as the delamination of composite structures with a contaminated interface layer; see, e.g., [6,7] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On variational-hemivariational inequalities with nonconvex constraints

2021

J. Nonlinear Var. Anal.

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“…[36,8,21] for contact and obstacle problems, and extended to the hp-setting in e.g. [30,31,34,3,4,5,2] and extended to the even more complicated class of hemivariational inequalities in [32]. In this paper we use a weak formulation not based on the Poincaré-Steklov operator but based on the entire Calderón projector, which leads to a slightly different stabilization term compared to [1].…”

Section: Introductionmentioning

confidence: 99%

Improved stabilization technique for frictional contact problems solved with hp-BEM

Banz,

Milicic,

Ovcharova

2018

Preprint

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We improve the residual based stabilization technique for Signorini contact problems with Tresca friction in linear elasticity solved with hp-mixed BEM which has been recently analyzed by Banz et al. in Numer. Math. 135 (2017) pp. 217-263. The stabilization allows us to circumvent the discrete inf-sup condition and thus the primal and dual sets can be discretized independently. Compared to the above mentioned paper we are able to remove the dependency of the scaling parameter on the unknown Sobolev regularity of the exact solution and can thus also improve the convergence rate in the a priori error estimate. The second improvement is a rigorous a priori and a posteriori error analysis when the boundary integral operators in the stabilization term are approximated. The latter is of fundamental importance to keep the computational time small. We present numerical results in two and three dimensions to underline our theoretical findings, show the superiority of the hp-adaptive stabilized mixed scheme and the effect induced by approximating the stabilization term. Moreover, we show the applicability of the proposed method to the Coulomb frictional case for which we extend the a posteriori error analysis.

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Coupling regularization and adaptive hp-BEM for the solution of a delamination problem

Cited by 15 publications

References 37 publications

Coupling of finite element and boundary element methods with regularization for a nonlinear interface problem with nonmonotone set-valued transmission conditions

Coupling of finite element and boundary element methods with regularization for a nonlinear interface problem with nonmonotone set-valued transmission conditions

On variational-hemivariational inequalities with nonconvex constraints

Improved stabilization technique for frictional contact problems solved with hp-BEM

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