Convergence analysis of a nonconforming finite element method solving a plate with ribs
Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law
In this paper, the convergence of a Neumann-Dirichlet algorithm to approximate Coulomb's contact problem between two elastic bodies is proved in a continuous setting. In this algorithm, the natural interface between the two bodies is retained as a decomposition zone.
Convergence of a Penalty-Finite Element Approximation for an Obstacle Problem.
Convergence of an equilibrium finite element model for plane elastostatics
An equilibrium triangular block-element, proposed by Watwood and Hartz, is subjected to an analysis and its approximability property is proved. If the solution is regular enough, a quasi-optimal error estimate follows for the dual approximation to the mixed boundary value problem of elasticity (based on Castigliano's principle). The convergence is proved even in a general case, when the solution is not regular.
Convergence of Mixed Finite Element Approximations for the Shallow Arch Problem.
Convergence of the finite element method applied to an anisotropic phase-field model
We formulate a finite element method for the computation of solutions to an anisotropic phase-field model for a binary alloy. Convergence is proved in the -norm. The convergence result holds for anisotropy below a certain threshold value. We present some numerical experiments verifying the theoretical results. For anisotropy below the threshold value we observe optimal order convergence, whereas in the case where the anisotropy is strong the numerical solution to the phase-field equation does not...
Convergence of the Nonconforming Wilson Element for Arbitrary Quadrilateral Meshes.
Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition
The problem of modeling acoustic waves scattered by an object with Neumann boundary condition is considered. The boundary condition is taken into account by means of the fictitious domain method, yielding a first order in time mixed variational formulation for the problem. The resulting system is discretized with two families of mixed finite elements that are compatible with mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not always correctly...
Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition
The problem of modeling acoustic waves scattered by an object with Neumann boundary condition is considered. The boundary condition is taken into account by means of the fictitious domain method, yielding a first order in time mixed variational formulation for the problem. The resulting system is discretized with two families of mixed finite elements that are compatible with mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not always...
Deterioration of a finite element method for arch structures when the thickness goes to zero.
Development of a finite-element-based design sensitivity analysis for buckling and postbuckling of composite plates.
Discrete forms of Friedrichs' inequalities in the finite element method
Discretization by Finite Elements of a Model Parameter Dependent Problem.
Discretization of the Timoshenko Beam Probelm by the p and the h-p Versions of the Finite Element Method.
Dynamic frictional contact of a viscoelastic beam
In this paper, we study the dynamic frictional contact of a viscoelastic beam with a deformable obstacle. The beam is assumed to be situated horizontally and to move, in both horizontal and tangential directions, by the effect of applied forces. The left end of the beam is clamped and the right one is free. Its horizontal displacement is constrained because of the presence of a deformable obstacle, the so-called foundation, which is modelled by a normal compliance contact condition. The effect...
Effective computation of restoring force vector in finite element method
We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and...
Efficient application of e-invariants in finite element method for an elastodynamic equation
We introduce a new efficient way of computation of partial differential equations using a hybrid method composed from FEM in space and FDM in time domain. The overall computational scheme is explicit in time. The key idea of the suggested way is based on a transformation of standard basis functions into new basis functions. The results of this matrix transformation are e-invariants (effective invariants) with such suitable properties which save the number of arithmetical operations needed for a...
Equilibrium Finite Elements for the Linear Elastic Problem.
Error estimates for elasto-plastic problems
Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem
This paper deals with an initial and boundary value problem describing the quasistatic evolution of rate-type viscoplastic materials. Using a fixed point property, an iterative method in the study of this problem is proposed. A concrete algorithm as well as some numerical results in the one-dimensional case are also presented.