A-posteriori Error Analysis for Linearization of Nonlinear Elliptic Problems and Their Discretizations
نویسنده
چکیده
The paper is devoted to a-posteriori quantitative analysis for errors caused by linearization of nonlinear elliptic boundary value problems and their nite element realizations. We employ duality theory in convex analysis to derive computable bounds on the diierence between the solution of a nonlinear problem and the solution of the linearized problem, by using the solution of the linearized problem only. We also derive computable bounds on diierences between nite element solutions of the nonlinear problem and nite element solutions of the linearized problem, by using nite element solutions of the linearized problem only. Numerical experiments show that our a-posteriori error bounds are eecient.
منابع مشابه
A posteriori error estimates for nonlinear problems. Lr-estimates for finite element discretizations of elliptic equations
— We extend the gênerai framework of [18] for deriving a posteriori error estimâtes for approximate solutions of noniinear elliptic problems such ihat it also yields L'-error estimâtes. The gênerai results are applied to finite element discretizations of scalar quasilinear elliptic pdes of 2nd order and the stationary incompressible Navier-Stokes équations. They immediately yield a posteriori e...
متن کاملAn a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow
In this paper we derive an a posteriori error estimate for the numerical approximation of the solution of a system modeling the flow of two incompressible and immiscible fluids in a porous medium. We take into account the capillary pressure, which leads to a coupled system of two equations: parabolic and elliptic. The parabolic equation may become degenerate, i.e., the nonlinear diffusion coeff...
متن کاملElliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems
It is known that the energy technique for a posteriori error analysis of finite element discretizations of parabolic problems yields suboptimal rates in the norm L∞(0, T ; L2(Ω)). In this paper we combine energy techniques with an appropriate pointwise representation of the error based on an elliptic reconstruction operator which restores the optimal order (and regularity for piecewise polynomi...
متن کاملEnergy Norm a Posteriori Error Estimation of Hp - Adaptive Discontinuous Galerkin Methods for Elliptic Problems
In this paper, we develop the a posteriori error estimation of hp-version interior penalty discontinuous Galerkin discretizations of elliptic boundary-value problems. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The bounds are explicit in the local mesh sizes and approximation orders. A series of numerical experiments il...
متن کاملAdaptive Multilevel Techniques for Mixed Finite Element Discretizations of Elliptic Boundary Value Problems Technische Universit at M Unchen Cataloging Data : Adaptive Multilevel Techniques for Mixed Finite Element Discretizations of Elliptic Boundary Value Problems
We consider mixed nite element discretizations of linear second order elliptic boundary value problems with respect to an adaptively generated hierarchy of possibly highly nonuniform simplicial triangula-tions. By a well known postprocessing technique the discrete problem is equivalent to a modiied nonconforming discretization which is solved by preconditioned cg-iterations using a multilevel B...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994