Error Estimates of a Galerkin Method for Some Nonlinear Sobolev Equations in one Space Dimension.
Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain with a nonlocal boundary condition. A Dirichlet BC containing an unknown additive constant, accompanied with a nonlocal (integral) Neumann side condition is prescribed at some boundary part . The rest of the boundary is equipped with Dirichlet or nonlinear Robin type BC. The solution is found via linearization. We design a robust and efficient approximation scheme. Error estimates for the linearization...
Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain with a nonlocal boundary condition. A Dirichlet BC containing an unknown additive constant, accompanied with a nonlocal (integral) Neumann side condition is prescribed at some boundary part Γn. The rest of the boundary is equipped with Dirichlet or nonlinear Robin type BC. The solution is found via linearization. We design a robust and efficient approximation scheme. Error estimates for...
Error estimation and adaptivity for nonlinear FE analysis
An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no flux splitting is required. The adaptive strategy is illustrated by means of a complex nonlinear problem:...
Error estimation and optimization of the functional algorithms of a random walk on a grid which are applied to solving the Dirichlet problem for the Helmholtz equation.
Error-Bounds for Finite Element Method.
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 the Effect of Numerical Integration in Finite Element Eigenvalue Approximation.
Estimations d'erreur pour des éléments finis droits presque dégénérés
Étude de deux schémas numériques pour les équations de la thermoélasticité
Exact, approximate solutions and error bounds for coupled implicit systems of partial differential equations.
Existence de maillages optimaux dans les méthodes d'éléments finis
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 .
Extrapolation Methods for Spline Collocation Solutions of Pseudodifferential Equations on Curves.