The paper reports some results on computational plasticity obtained within the Special Research Program “Numerical and Symbolic Scientific Computing” and within the Doctoral Program “Computational Mathematics” both supported by the Austrian Science Fund FWF under the grants SFB F013 and DK W1214, respectively. Adaptivity and fast solvers are the ingredients of efficient numerical methods. The p...

An anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is considered. The adaptation method generates anisotropic adaptive meshes as quasiuniform ones in some metric space. The associated metric tensor is computed by means of a posteriori hierarchical error estimates. A global hierarchical error estimate is employed in this study to obtain reliabl...

Superconvergence of order O(h), for some ρ > 0, is established for the gradient recovered with the Polynomial Preserving Recovery (PPR) when the mesh is mildly structured. Consequently, the PPR-recovered gradient can be used in building an asymptotically exact a posteriori error estimator.

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

We consider discretizations of linear parabolic equations by A-stable θ-schemes in time and conforming finite elements in space. For these discretizations we derive a residual a posteriori error estimator. The estimator yields upper bounds on the error which are global in space and time and lower bounds that are global in space and local in time. The error estimates are fully robust in the sens...

We study a posteriori error estimates in the energy norm for some parabolic obstacle problems discretized with a Euler implicit time scheme combined with a finite element spatial approximation. We discuss the reliability and efficiency of the error indicators, as well as their localization properties. Apart from the obstacle resolution, the error indicators vanish in the so-called full contact ...

In this paper, a new a posteriori error estimator for nonconforming convection diffusion approximation problem, which relies on the small discrete problems solution in stars, has been established. It is equivalent to the energy error up to data oscillation without any saturation assumption nor comparison with residual estimator.

We derive hierarchical a posteriori error estimates for elliptic variational inequalities. The evaluation amounts to the solution of corresponding scalar local subproblems. We derive some upper bounds for the e ectivity rates and the numerical properties are illustrated by typical examples.

We analyze a posteriori error estimators for finite element discretizations of convec-tion-dominated stationary convection-diffusion equations using locally refined, isotropic meshes. The estimators are based on either the evaluation of local residuals or the solution of discrete local problems with Dirichlet or Neumann boundary conditions. All estimators yield global upper and lower bounds for...

In this paper, we develop a priori and a posteriori error estimates for wavelet-Taylor– Galerkin schemes introduced in Refs. 6 and 7 (particularly wavelet Taylor–Galerkin scheme based on Crank–Nicolson time stepping). We proceed in two steps. In the first step, we construct the priori estimates for the fully discrete problem. In the second step, we construct error indicators for posteriori esti...