On numerical solution of the Dirichlet problem by the method of locally-canonical decomposition.
On numerical solution of weight minimization of elastic bodies weakly supporting tension
Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its weight and to the hydrostatic pressure. A part of the boundary has to be found so as to minimize a given cost functional. The numerical realization using a penalty method and finite element technique is presented. Some typical results are shown.
On Patched Variational Principles with Application to Elliptic and Mixed Elliptic-Hyperbolic Problems.
On phase segregation in nonlocal two-particle Hartree systems
We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical investigation visualizes the approach to this segregated regime.
On polynomial robustness of flux reconstructions
We deal with the numerical solution of elliptic not necessarily self-adjoint problems. We derive a posteriori upper bound based on the flux reconstruction that can be directly and cheaply evaluated from the original fluxes and we show for one-dimensional problems that local efficiency of the resulting a posteriori error estimators depends on only, where is the discretization polynomial degree. The theoretical results are verified by numerical experiments.
On preconditioning Schur complement and Schur complement preconditioning.
On projection-difference analogues of the identity operator
On quadrature methods for the double layer potential equation over the boundary of a polyhedron.
On real interpolation, finite differences, and estimates depending on a parameter for discretizations of elliptic boundary value problems.
On reducing bandwidth of matrices in the Go-Away algorithm for regular grids.
On Richardson Extrapolation for Finite Difference Methods on Regular Grids.
On selection of interface weights in domain decomposition methods
Different choices of the averaging operator within the BDDC method are compared on a series of 2D experiments. Subdomains with irregular interface and with jumps in material coefficients are included into the study. Two new approaches are studied along three standard choices. No approach is shown to be universally superior to others, and the resulting recommendation is that an actual method should be chosen based on properties of the problem.
On semiregular families of triangulations and linear interpolation
We consider triangulations formed by triangular elements. For the standard linear interpolation operator we prove the interpolation order to be for provided the corresponding family of triangulations is only semiregular. In such a case the well-known Zlámal’s condition upon the minimum angle need not be satisfied.
On shooting methods for the discrete Helmholtz equation with constant coefficients.
On singularities of capillary surfaces in the absence of gravity.
On solution to an optimal shape design problem in 3-dimensional linear magnetostatics
In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization...
On Some Boundary Element Methods for the Heat Equation.
On Some Finite Element Procedures for Solving Second Order Boundary Value Problems.
On Some High Accuracy Difference Schemes for Solving Elliptic Equations.
On some implicit and semi-implicit staggered schemes for the shallow water and Euler equations
In this paper, we propose implicit and semi-implicit in time finite volume schemes for the barotropic Euler equations (hence, as a particular case, for the shallow water equations) and for the full Euler equations, based on staggered discretizations. For structured meshes, we use the MAC finite volume scheme, and, for general mixed quadrangular/hexahedral and simplicial meshes, we use the discrete unknowns of the Rannacher−Turek or Crouzeix−Raviart finite elements. We first show that a solution...