A <i>p</i>‐adaptive algorithm for the BEM with the hypersingular operator on the plane screen

“…For the error estimation of the auxiliary variational equality problem in a three dimensional setting we refer to [28]. Combining Theorems 7 and 11 yields the following result.…”

Section: Bubble Enriched Based Error Estimationmentioning

confidence: 91%

Onhp-adaptive BEM for frictional contact problems in linear elasticity

Banz

Stephan

2015

Computers & Mathematics with Applications

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Tresca/Coulomb frictional contact problem hp-adaptive BEM Residual and bubble a posteriori error estimates a b s t r a c t A mixed formulation for a Tresca frictional contact problem in linear elasticity is considered in the context of boundary integral equations, which is later extended to Coulomb friction. The discrete Lagrange multiplier, an approximation of the surface traction on the contact boundary part, is a linear combination of biorthogonal basis functions. In case of curved (isoparametric) elements, these are the solutions of local problems. In particular, the biorthogonality allows to rewrite the variational inequality constraints as a simple set of complementarity problems. Thus, enabling an efficient application of a semi-smooth Newton solver for the discrete mixed problem, converging locally super-linearly in the frictional case and quadratically in the frictionless case. Typically, the solution of frictional contact problems is of reduced regularity at the interface between contact to non-contact and from stick to slip. To identify the a priori unknown locations of these interfaces two a posteriori error estimations are introduced. In a first step the error is split into specific error contributions resulting from the contact and friction conditions and from the discretization error of a variational equation. For the latter a residual and a bubble error estimation are considered explicitly. The numerical experiments show the applicability of the derived error estimations and the superiority of hp-adaptivity compared to low order uniform and adaptive approaches.

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“…Numerical results for this algorithm are presented in [6] and [7] for a hypersingular integral equation on a surface piece modeling a scalar screen problem in R 3 ; the resulting hp-refinements give suitably refined meshes together with appropriate distributions of polynomial degrees. The corresponding implementation for the eddy current problem above can be performed with the program package maiprogs [13]; for the pure h-version corresponding numerical experiments are given in [20].…”

Section: Compute the Galerkin Solution 2 For Each Element T ∈ T H Cmentioning

confidence: 99%

An hp-adaptive finite element/boundary element coupling method for electromagnetic problems

2006

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We present an hp-version of the finite element / boundary element coupling method to solve the eddy current problem for the time-harmonic Maxwell's equations. We use H(curl, )-conforming vector-valued polynomials to approximate the electric field in the conductor and surface curls of continuous piecewise polynomials on the boundary of to approximate the twisted tangential trace of the magnetic field on . We present both a priori and a posteriori error estimates together with a three-fold hp-adaptive algorithm to compute the fem/bem coupling solution with appropriate distributions of polynomial degrees on suitably refined meshes.

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A p‐adaptive algorithm for the BEM with the hypersingular operator on the plane screen

Cited by 15 publications

References 16 publications

A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains

A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains

Onhp-adaptive BEM for frictional contact problems in linear elasticity

An hp-adaptive finite element/boundary element coupling method for electromagnetic problems

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