On boundary integral equations of the first kind for the bi-laplacian in a polygonal plane domain
On convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations.
On Some Boundary Element Methods for the Heat Equation.
On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations
We prove the convergence of polynomial collocation method for periodic singular integral, pseudodifferential and the systems of pseudodifferential equations in Sobolev spaces via the equivalence between the collocation and modified Galerkin methods. The boundness of the Lagrange interpolation operator in this spaces when allows to obtain the optimal error estimate for the approximate solution i.e. it has the same rate as the best approximation of the exact solution by the polynomials.
On the bicubic spline collocation method for Poisson's equations.
On the Boundary Element Method for Some Nonlinear Boundary Value Problems.
On the convergence of SCF algorithms for the Hartree-Fock equations
On the convergence of SCF algorithms for the Hartree-Fock equations
The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting algorithm is proved to be well-posed and to converge provided the shift parameter is large enough. On the contrary, cases when the Roothaan algorithm is not well defined or fails in converging are exhibited. These mathematical results are confronted to numerical experiments performed by chemists.
On the Convergence of the Galerkin Method for Nonsmooth Solutions of Integral Equations.
On the coupled BEM and FEM for a nonlinear exterior Dirichlet problem in R2.
On the Fast Matrix Multiplication in the Boundary Element Method by Panel Clustering.
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 method of least squares on the boundary
On the order of pointwise convergence of some boundary element methods. Part I. Operators of negative and zero order
On the super-approximation property of Galerkin's method with finite elements.