Adaptive FE–BE coupling for strongly nonlinear transmission problems with Coulomb friction

TY - JOUR

T1 - Adaptive FE–BE coupling for strongly nonlinear transmission problems with Coulomb friction

AU - Gimperlein, Heiko

AU - Maischak, Matthias

AU - Schrohe, Elmar

AU - Stephan, Ernst P.

PY - 2011/2

Y1 - 2011/2

N2 - We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction, where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation on the exterior domain. The problem is reduced to a boundary/domain variational inequality, a discretized saddle point formulation of which is then solved using the Uzawa algorithm and adaptive mesh refinements based on a gradient recovery scheme. The Galerkin approximations are shown to converge to the unique solution of the variational problem in a suitable product of Lp- and L2-Sobolev spaces.

AB - We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction, where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation on the exterior domain. The problem is reduced to a boundary/domain variational inequality, a discretized saddle point formulation of which is then solved using the Uzawa algorithm and adaptive mesh refinements based on a gradient recovery scheme. The Galerkin approximations are shown to converge to the unique solution of the variational problem in a suitable product of Lp- and L2-Sobolev spaces.

M3 - Journal article

SN - 0029-599X

VL - 117

SP - 307

EP - 332

JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 2

ER -