On the Efficient Solution of Nonlinear Finite Element Equations I.
On the efficient use of the Galerkin-method to solve Fredholm integral equations
In the present paper we describe, how to use the Galerkin-method efficiently in solving boundary integral equations. In the first part we show how the elements of the system matrix can be computed in a reasonable time by using suitable coordinate transformations. These techniques can be applied to a wide class of integral equations (including hypersingular kernels) on piecewise smooth surfaces in 3-D, approximated by spline functions of arbitrary degree. In the second part we show, how to use the...
On the equivalence of primal and dual substructuring preconditioners.
On the evaluation of finite element sensitivities to nodal coordinates.
On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs
The existence and the unicity of a weak solution of the boundary value problem for a shallow shell reinforced with stiffening ribs is proved by the direct variational method. The boundary value problem is solved in the space , on which the corresponding bilinear form is coercive. A finite element method for numerical solution is introduced. The approximate solutions converge to a weak solution in the space .
On the existence of strongly regular families of triangulations for domains with a piecewise smooth boundary
In this note we present an algorithm for a construction of strongly regular families of triangulations for planar domains with a piecewise curved boundary. Some additional properties of the resulting triangulations are considered.
On the Extrapolation of Galerkin Methods for Parabolic Problems.
On the Fast Matrix Multiplication in the Boundary Element Method by Panel Clustering.
On the Fast Solutions of Nonlinear Elliptic Equations.
On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains
The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition considered in a two-dimensional nonpolygonal domain with a curved boundary. The existence and uniqueness of the solution of the continuous problem is a consequence of the monotone operator theory. The main attention is paid to the effect of the basic finite element variational crimes: approximation of the curved boundary by a polygonal one and the evaluation of integrals by numerical...
On the Finite Element Approximation of a Cascade Flow Problem.
On the finite element approximation of solutions for radiation problem
On the Finite Element Method.
On the finite volume element method.
On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes
We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with Qr-elements for the velocity and discontinuous -elements for the pressure where the order r can vary from element to element between 2 and a fixed bound . We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes.
On the Maxwell's system in composite media
On the method of fictitious domains for a fourth order quasilinear elliptic equation. (Sur la méthode des domaines fictifs pour une équation elliptique quasilinéaire du quatrième ordre.)
On the method of least squares on the boundary
On the multi-grid iteration for the eigenvalue problem and the degree of interpolation wich it requires (I).
On the Multigrid Solution of Finite Element Equations With Isoparametric Elements.