Estimates for spline projections
Estimates from above and from below for the Homogenized Coefficients.
Estimation de l'erreur d'interpolation d'Hermite dans IR".
Estimation de l'erreur sur le coefficient de la singularité de la solution d'un problème elliptique sur un ouvert avec coin
Estimation d'erreur optimale et de type superconvergence de la méthode des éléments finis pour un problème aux limites, dégénéré
Estimation of EDZ zones in great depths by elastic-plastic models
This contribution is devoted to modeling damage zones caused by the excavation of tunnels and boreholes (EDZ zones) in connection with the issue of deep storage of spent nuclear fuel in crystalline rocks. In particular, elastic-plastic models with Mohr-Coulomb or Hoek-Brown yield criteria are considered. Selected details of the numerical solution to the corresponding problems are mentioned. Possibilities of elastic and elastic-plastic approaches are illustrated by a numerical example.
Estimation of the Effect of Numerical Integration in Finite Element Eigenvalue Approximation.
Estimations d'erreur pour des éléments finis droits presque dégénérés
Estimations des erreurs de meilleure approximation polynomiale et d'interpolation de Lagrange dans les espaces de Sobolev d'ordre non entier.
Evaluation of the condition number in linear systems arising in finite element approximations
This paper derives upper and lower bounds for the -condition number of the stiffness matrix resulting from the finite element approximation of a linear, abstract model problem. Sharp estimates in terms of the meshsize h are obtained. The theoretical results are applied to finite element approximations of elliptic PDE's in variational and in mixed form, and to first-order PDE's approximated using the Galerkin–Least Squares technique or by means of a non-standard Galerkin technique in L1(Ω). Numerical...
Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows
In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved for small relaxation times. Continuous piecewise linear finite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and a priori error estimates are established using a Newton-chord fixed point theorem, a posteriori error estimates are also derived....
Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows
In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved for small relaxation times. Continuous piecewise linear finite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and a priori error estimates are established using a Newton-chord fixed point theorem, a posteriori error estimates are also derived. An...
Existence and Approximation Results for Nonlinear Mixed Problems : Application to Incompressible Finite Elasticity.
Existence de maillages optimaux dans les méthodes d'éléments finis
Existence of nontrivial solution for a nonlocal elliptic equation with nonlinear boundary condition.
Existence of solutions to singular elliptic equations with convection terms via the Galerkin method.
Expanded mixed finite element methods for linear second-order elliptic problems, I
Expanded mixed finite element methods for quasilinear second order elliptic problems, II
Explicit estimation of error constants appearing in non-conforming linear triangular finite element method
The non-conforming linear () triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both the theoretical and practical purposes. Since various error constants must be quantitatively evaluated for its accurate a priori and a posteriori error estimates, we derive their theoretical upper bounds and some computational results. In particular, the Babuška-Aziz maximum angle condition is required just as in the case of the conforming triangle. Some applications...
Explicit finite element error estimates for nonhomogeneous Neumann problems
The paper develops an explicit a priori error estimate for finite element solution to nonhomogeneous Neumann problems. For this purpose, the hypercircle over finite element spaces is constructed and the explicit upper bound of the constant in the trace theorem is given. Numerical examples are shown in the final section, which implies the proposed error estimate has the convergence rate as .