Fehlerabschätzungen für das Galerkinverfahren zur Lösung von Evolutionsgleichungen.
FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity
We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is...
FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity
We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is...
Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem
We extend our results on fictitious domain methods for Poisson’s problem to the case of incompressible elasticity, or Stokes’ problem. The mesh is not fitted to the domain boundary. Instead boundary conditions are imposed using a stabilized Nitsche type approach. Control of the non-physical degrees of freedom, i.e., those outside the physical domain, is obtained thanks to a ghost penalty term for both velocities and pressures. Both inf-sup stable and stabilized velocity pressure pairs are considered....
Filter factor analysis of an iterative multilevel regularizing method.
Finite difference approximation to the Cauchy problem for non-linear parabolic differential equations
Finite difference approximations for partial differential equations with rapidly oscillating coefficients
Finite Difference Approximations to the Dirichlet Problem for Elliptic Systems.
Finite difference methods for coupled flow interaction transport models.
Finite Dimensional Approximation of Bifurcation Problems in Presence of Symmetries.
Finite Dimensional Approximation of Nonlinear Problems. Part I. Branches of Nonsingular Solutions.
Finite Dimensional Approximation of Nonlinear Problems. Part II : Limit Points.
Finite Dimensional Approximation of Nonlinear Problems. Part III : Simple Bifurcation Points.
Finite element analysis for unilateral problems with obstacles on the boundary
Finite element analysis of unilateral problems with obstacles on the boundary is given. Provided the exact solution is smooth enough, we obtain the rate of convergence for the case of one and two (lower and upper) obstacles on the boundary. At the end of this paper the proof of convergence without any regularity assumptions on the exact solution is given.
Finite element analysis of a static contact problem with Coulomb friction
A unilateral contact problem with a variable coefficient of friction is solved by a simplest variant of the finite element technique. The coefficient of friction may depend on the magnitude of the tangential displacement. The existence of an approximate solution and some a priori estimates are proved.
Finite element analysis of free material optimization problem
Free material optimization solves an important problem of structural engineering, i.e. to find the stiffest structure for given loads and boundary conditions. Its mathematical formulation leads to a saddle-point problem. It can be solved numerically by the finite element method. The convergence of the finite element method can be proved if the spaces involved satisfy suitable approximation assumptions. An example of a finite-element discretization is included.
Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary
The Poisson equation with non-homogeneous unilateral condition on the boundary is solved by means of finite elements. The primal variational problem is approximated on the basis of linear triangular elements, and -convergence is proved provided the exact solution is regular enough. For the dual problem piecewise linear divergence-free approximations are employed and -convergence proved for a regular solution. Some a posteriori error estimates are also presented.
Finite element analysis of sloshing and hydroelastic vibrations under gravity
This paper deals with a finite element method to solve fluid-structure interaction problems. More precisely it concerns the numerical computation of harmonic hydroelastic vibrations under gravity. It is based on a displacement formulation for both the fluid and the solid. Gravity effects are included on the free surface of the fluid as well as on the liquid-solid interface. The pressure of the fluid is used as a variable for the theoretical analysis leading to a well posed mixed linear eigenvalue...
Finite element analysis of the Signorini problem
Finite element analysis of the Signorini problem in semi-coercive cases
The plane Signorini problem is considered in the cases, when there exist non-trivial rigid admissible displacements. The existence and uniqueness of the solution and the convergence of piecewise linear finite element approximations is discussed.