Adaptive hp-FEM for the Contact Problem with Tresca Friction in Linear Elasticity: The Primal-dual Formulation and a Posteriori Error Estimation
نویسندگان
چکیده
We present an a priori analysis of the hp-version of the finite element method for the primal-dual formulation of frictional contact in linear elasticity. We employ a novel hp-mortar projection operator, which is uniformly stable in the mesh width and grows slowly in the polynomial degree. We derive an hp-FEM residual error indicator, develop an hp-adaptive strategy that is based on testing for analyticity, and show in numerical examples that the adaptive algorithm can lead to exponential rates of convergence.
منابع مشابه
Adaptive hp-FEM for the Contact Problem with Tresca Friction in Linear Elasticity: The Primal Formulation
We present an a priori analysis of the hp-version of the finite element method for the primal formulation of frictional contact in linear elasticity. We introduce a new limiting case estimate for the interpolation error at Gauss and Gauss-Lobatto quadrature points. An hp-adaptive strategy is presented; numerical results shows that this strategy can lead to exponential convergence.
متن کاملOn hp-adaptive BEM for frictional contact problems in linear elasticity
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 elements, these are the solut...
متن کاملStabilized mixed hp-BEM for frictional contact problems in linear elasticity
We analyze stabilized mixed hp-boundary element methods for frictional contact problems for the Lamé equation. The stabilization technique circumvents the discrete inf-sup condition for the mixed problem and thus allows us to use the same mesh and polynomial degree for the primal and dual variables. We prove a priori convergence rates in the case of Tresca friction, using Gauss-Legendre-Lagrang...
متن کاملMixed Fem of Higher Order for Contact Problems with Friction
This paper presents a mixed variational formulation and its discretization by finite elements of higher-order for the Signorini problem with Tresca friction. To guarantee the unique existence of the solution to the discrete mixed problem, a discrete inf-sup condition is proved. Moreover, a solution scheme based on the dual formulation of the problem is proposed. Numerical results confirm the th...
متن کاملOn Domain Decomposition Algorithms for Contact Problems with Tresca Friction
Development of numerical methods for the solution of contact problems is a challenging task whose difficulty lies in the non-linear conditions for non-penetration and friction. Recently, many authors proposed to use various numerical algorithms combined with multigrid or domain decomposition techniques; see, e.g., the primal-dual active set algorithm [8], the non-smooth multiscale method [10], ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009