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We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. The major loops in the code have been vectorized using the so called array operation in MATLAB, and no low level languages like the C or Fortran has been used for the purpose. The implementation is based on having the vectorization part separated, in(More)
We discuss a solution algorithm for quasi-static elastoplastic problems with hardening. Such problems can be described by a time dependent variational inequality, where the displacement and the plastic strain fields serve as primal variables. After discretization in time, one variational inequality of the second kind is obtained per time step and can be(More)
The boundary value problem representing one time step of the primal formulation of elastoplasticity with positive hardening leads to a variational inequality of the second kind with some non-differentiable functional. This paper establishes an adaptive finite element algorithm for the solution of this variational inequality that yields the energy reduction(More)
We consider a Poisson boundary value problem and its functional a posteriori error estimate derived by S. Repin in 1999. The estimate majorizes the H1 seminorm of the error of the discrete solution computed by FEM method and contains a free ux variable from the H div space. In order to keep the estimate sharp, a procedure for the minimization of the(More)
The quasi-static evolution of an elastoplastic body with a multi-surface constitutive law of linear kinematic hardening type allows the modeling of curved stress-strain relations. It generalizes classical small-strain elastoplasticity from one to various plastic phases. This paper presents the mathematical models and proves existence and uniqueness of the(More)
Abstract: Based on the ideas of the paper [8] by Talal Rahman and Jan Valdman we propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in discretizations of H (div) spaces and Nédélec elements in(More)
Multi-yield elastoplasticity models a material with more than one plastic state and hence allows for refined approximation of irreversible deformations. Aspects of the mathematical modeling and a proof of unique existence of weak solutions can be found in part I of this paper [BCV04]. In this part II we establish a canonical time-space discretization of the(More)
In this paper, we consider variational inequalities related to problems with nonlinear boundary conditions. We are focused on deriving a posteriori estimates of the difference between exact solutions of such type variational inequalities and any function lying in the admissible functional class of the problem considered. These estimates are obtained by an(More)
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(More)
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error(More)