On the Convergence of Multi-Grid Methods with Transforming Smoothers. Theory with Applications to the Navier-Stokes Equations.
On the convergence of numerical schemes for the Boltzmann equation
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 solutions of random differential equations
On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem
Si discretizza il problema dell'ostacolo parabolico con differenze all'indietro nel tempo ed elementi finiti lineari nello spazio e si dimostrano stime dell'errore per la frontiera libera discreta.
On the convergence of the backward Euler algorithm for the multidimensional heat equation
The backward Euler algorithm for the multidimensional nonhomogeneous heat equation is analyzed, based on the finite element method. The existence and uniqueness of the numerical solution is investigated. Also, the convergence of the numerical solutions is studied.
On the Convergence of the Conjugate Gradient Method for Singular Capacitance Matrix Equations from the Neumann Problem of the Poisson Equation.
On the Convergence of the Galerkin Method for Nonsmooth Solutions of Integral Equations.
On the convergence of the stochastic Galerkin method for random elliptic partial differential equations
In this article we consider elliptic partial differential equations with random coefficients and/or random forcing terms. In the current treatment of such problems by stochastic Galerkin methods it is standard to assume that the random diffusion coefficient is bounded by positive deterministic constants or modeled as lognormal random field. In contrast, we make the significantly weaker assumption that the non-negative random coefficients can be bounded strictly away from zero and infinity by random...
On the Convergence Rate Estimates for Finite Difference Schemes Approximating Homogeneous Initial-boundary Value Problem for Hyperbolic Equation
On the convergence rate of spectral approximation for the equations for nonhomogeneous asymmetric fluids
On the convolution equations over the quarter-plane.
On the correct formulation of a multidimensional problem for strictly hyperbolic equations of higher order.
On the correctness of the Dirichlet problem in a characteristic rectangle for fourth order linear hyperbolic equations.
On the cost of null-control of an artificial advection-diffusion problem
In this paper we study the null-controllability of an artificial advection-diffusion system in dimension n. Using a spectral method, we prove that the control cost goes to zero exponentially when the viscosity vanishes and the control time is large enough. On the other hand, we prove that the control cost tends to infinity exponentially when the viscosity vanishes and the control time is small enough.
On the coupled BEM and FEM for a nonlinear exterior Dirichlet problem in R2.
On the coupled system of nonlinear wave equations with different propagation speeds
On the coupling of finite elements and boundary elements for transonic potential flow computations
On the critical Neumann problem with lower order perturbations
We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent and lower order perturbations in bounded domains. Solutions are obtained by min max methods based on a topological linking. A nonlinear perturbation of a lower order is allowed to interfere with the spectrum of the operator -Δ with the Neumann boundary conditions.