On the Approximate Solution of Nonlinear Variational Inequalities.
On the approximation of a quasilinear mixed problem
On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at different levels of accuracy (after an empirical interpolation procedure). The successive constraint method is applied on the coarse level to obtain a lower bound for the stability factors, and this bound is extended to the fine level by adding a proper...
On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at different levels of accuracy (after an empirical interpolation procedure). The successive constraint method is applied on the coarse level to obtain a lower bound for the stability factors, and this...
On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at different levels of accuracy (after an empirical interpolation procedure). The successive constraint method is applied on the coarse level to obtain a lower bound for the stability factors, and this...
On the Construction of Finite Difference Schemes Approximating Generalized Solutions
On the convergence of a modified block SOR algorithm.
On the Convergence of Difference Schemes for the Approximation of Solutions u...W... (m>0.5) of Elliptic Equations with Mixed Derivatives.
On the convergence of difference schemes for the equation on generalized solutions of .
On the Convergence of Finite Difference Scheme for Elliptic Equation With Coefficients Containing Dirac Distribution
On the Convergence of Finite-Difference Schemes for Parabolic Equations with Variable Coefficients.
On the convergence of generalized polynomial chaos expansions
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement...
On the convergence of generalized polynomial chaos expansions
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial...
On the convergence of multigrid methods for flow problems.
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 coupled BEM and FEM for a nonlinear exterior Dirichlet problem in R2.
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 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 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 numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation.