Sard Kernel Theorems on Triangular Domains with Application to Finite Element Error Bounds.
Schwarz alternating and iterative refinemnt methods for mixed formulations of elliptic problems, part I: algorithms and numerical results.
Schwarz alternating and iterative refinemnt methods for mixed formulations of elliptic problems, part II: convergence theory.
Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case
We propose and study some new additive, two-level non-overlapping Schwarz preconditioners for the solution of the algebraic linear systems arising from a wide class of discontinuous Galerkin approximations of elliptic problems that have been proposed up to now. In particular, two-level methods for both symmetric and non-symmetric schemes are introduced and some interesting features, which have no analog in the conforming case, are discussed. Both the construction and analysis of the proposed domain...
s∗-compressibility of the discrete Hartree-Fock equation
The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...
s∗-compressibility of the discrete Hartree-Fock equation
The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...
Second-Order Finite Element Approximations and a posteriori Error Estimation for Two-Dimensional Parabolic Systems.
Semidiscrete and single step fully discrete approximations for second order hyperbolic equations
Semiorthogonal linear prewavelets on irregular meshes
We extend results on constructing semiorthogonal linear spline prewavelet systems in one and two dimensions to the case of irregular dyadic refinement. In the one-dimensional case, we obtain sharp two-sided inequalities for the -condition, 1 < p < ∞, of such systems.
Semiregular finite elements in solving some nonlinear problems
In this paper, under the maximum angle condition, the finite element method is analyzed for nonlinear elliptic variational problem formulated in [4]. In [4] the analysis was done under the minimum angle condition.
Semiregular hermite tetrahedral finite elements
Tetrahedral finite -elements of the Hermite type satisfying the maximum angle condition are presented and the corresponding finite element interpolation theorems in the maximum norm are proved.
Several notes on the circumradius condition
Recently, the so-called circumradius condition (or estimate) was derived, which is a new estimate of the -error of linear Lagrange interpolation on triangles in terms of their circumradius. The published proofs of the estimate are rather technical and do not allow clear, simple insight into the results. In this paper, we give a simple direct proof of the case. This allows us to make several observations such as on the optimality of the circumradius estimate. Furthermore, we show how the case...
Shape optimization by means of the penalty method with extrapolation
A model shape optimal design in is solved by means of the penalty method with extrapolation, which enables to obtain high order approximations of both the state function and the boundary flux, thus offering a reliable gradient for the sensitivity analysis. Convergence of the proposed method is proved for certain subsequences of approximate solutions.
Shape optimization of an elasto-perfectly plastic body
Within the range of Prandtl-Reuss model of elasto-plasticity the following optimal design problem is solved. Given body forces and surface tractions, a part of the boundary, where the (two-dimensional) body is fixed, is to be found, so as to minimize an integral of the squared yield function. The state problem is formulated in terms of stresses by means of a time-dependent variational inequality. For approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant...
Shape optimization of an elasto-plastic body for the model with strain- hardening
The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences...
Shape optimization of elastic axisymmetric bodies
The shape of the meridian curve of an elastic body is optimized within a class of Lipschitz functions. Only axisymmetric mixed boundary value problems are considered. Four different cost functionals are used and approximate piecewise linear solutions defined on the basis of a finite element technique. Some convergence and existence results are derived by means of the theory of the appropriate weighted Sobolev spaces.
Shape optimization of elasto-plastic axisymmetric bodies
A minimization of a cost functional with respect to a part of a boundary is considered for an elasto-plastic axisymmetric body obeying Hencky's law. The principle of Haar-Kármán and piecewise linear stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.
Shape optimization of elasto-plastic bodies
Existence of an optimal shape of a deformable body made from a physically nonlinear material obeying a specific nonlinear generalized Hooke’s law (in fact, the so called deformation theory of plasticity is invoked in this case) is proved. Approximation of the problem by finite elements is also discussed.
Shape optimization of elastoplastic bodies obeying Hencky's law
A minimization of a cost functional with respect to a part of the boundary, where the body is fixed, is considered. The criterion is defined by an integral of a yield function. The principle of Haar-Kármán and piecewise constant stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.
Sharp L...-Error Estimates for Semilinear Elliptic Problems with Free Boundaries.