Analysis of a posteriori error estimates of the discontinuous Galerkin method for nonlinear ordinary differential equations
نویسنده
چکیده
Article history: Received 23 April 2015 Received in revised form 3 February 2016 Accepted 31 March 2016 Available online xxxx I would like to dedicate this work to my Father, Ahmed Baccouch, who unfortunately passed away during the completion of this work
منابع مشابه
Adaptive Finite Element Methods for Multiphysics Problems Adaptive Finite Element Methods for Multiphysics Problems
In this thesis we develop and evaluate the performance of adaptive finite element methods for multiphysics problems. In particular, we propose a methodology for deriving computable error estimates when solving unidirectionally coupled multiphysics problems using segregated finite element solvers. The error estimates are of a posteriori type and are derived using the standard framework of dual w...
متن کاملA posteriori error estimation for hp-version time-stepping methods for parabolic partial differential equations
The aim of this paper is to develop an hp-version a posteriori error analysis for the time discretization of parabolic problems by the continuous Galerkin (cG) and the discontinuous Galerkin (dG) time-stepping methods, respectively. The resulting error estimators are fully explicit with respect to the local time-steps and approximation orders. Their performance within an hp-adaptive refinement ...
متن کاملThe Discontinuous Galerkin Method for Two-dimensional Hyperbolic Problems Part II: A Posteriori Error Estimation
In this manuscript we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of scalar firstorder hyperbolic partial differential problems on triangular meshes. We explicitly write the basis functions for the error spaces corresponding to several finite element spaces. The leading term of the discretization error on each tr...
متن کاملA Posteriori Error Estimates for Nonlinear Problems. Finite Element Discretizations of Parabolic Equations
We give a general framework for deriving a posteriori error estimates for approximate solutions of nonlinear parabolic problems. In a first step it is proven that the error of the approximate solution can be bounded from above and from below by an appropriate norm of its residual. In a second step this norm of the residual is bounded from above and from below by a similar norm of a suitable fin...
متن کاملALGEBRAIC NONLINEARITY IN VOLTERRA-HAMMERSTEIN EQUATIONS
Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...
متن کامل