a non-linear finite element model could be a useful tool in the development of a method of predicting soil pressure-sinkage behaviour, and can be used to investigate and analyze soil compaction. this study was undertaken to emphasize that the finite element method (fem) is a proper technique to model soil pressure-sinkage behaviour. for this purpose, the finite element method was used to model ...

In this article we propose a unified analysis for conforming and non-conforming finite element methods that provides a partial answer to the problem of preserving discrete divergence constraints when computing numerical solutions to the time-dependent Maxwell system. In particular, we formulate a compatibility condition relative to the preservation of genuinely oscillating modes that takes the ...

We prove the convergence of a finite element method for the NavierStokes equations in which the no-slip condition, u ·τ i = 0 on Γ for i = 1, 2 is imposed by a penalty method and the no-penetration condition, u·n = 0 on Γ, is imposed by Lagrange multipliers. This approach has been studied for the Stokes problem in [2]. In most flows the Reynolds number is not This work partially supported by NS...

We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFEM) for second-order linear reaction-diffusion equations. To the best of our knowledge, the sharpest known error bounds for the hp-DGFEM are due to Riviére, Wheeler and Girault [8] and due to Houston, Schwab and Süli [5] which are optimal with respect to the meshsize h but suboptimal with respect to ...

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximat...

This paper deals with a study the linear finite element approximation of piezoelectric Signorini's contact problem and without friction. We derive error estimates that depend on penalty parameter ε mesh size h. Moreover, under some regularities solution to problems requirements parameters h, we provide results convergence rate penalized solution.

Contact problems in solid mechanics are traditionally solved using the h-version of the finite element method. The constraints are enforced along the surfaces of e.g. elastic bodies under consideration. Standard constraint algorithms include penalty methods, Lagrange multiplier methods and combinations thereof. For complex scenarios, a major part of the solution time is taken up by operations t...

In this paper the results in [S. Leyendecker, P. Betsch, P. Steinmann, Energy-conserving integration of constrained Hamiltonian systems—a comparison of approaches, Comput. Mech. 33 (2004) 174–185] are extended to geometrically exact beams. The finite element formulation for nonlinear beams in terms of directors, providing a framework for the objective description of their dynamics, is considere...

We consider a discontinuous Galerkin finite element method for the advection–reaction equation in two space–dimensions. For polynomial approximation spaces of degree greater than or equal to two on triangles we propose a method where stability is obtained by a penalization of only the upper portion of the polynomial spectrum of the jump of the solution over element edges. We prove stability in ...