Error estimates for a multidimensional meshfree Galerkin method with diffuse derivatives and stabilization

Error Estimates for a Discontinuous Galerkin Method with Interior Penalties Applied to Nonlinear Sobolev Equations

A Discontinuous Galerkin method with interior penalties is presented for nonlinear Sobolev equations. A semi-discrete and a family of fully-discrete time approximate schemes are formulated. These schemes are symmetric. Hp-version error estimates are analyzed for these schemes. For the semi-discrete time scheme a priori L∞(H 1) error estimate is derived and similarly, l∞(H 1) and l2(H 1) for the...

Fuzzy Galerkin method for solving Fredholm integral equations with error analysis

Energy norm error estimates for averaged discontinuous Galerkin methods: Multidimensional case

A mathematical analysis is presented for a class of interior penalty (IP) discontinuous Galerkin approximations of elliptic boundary value problems. In the framework of the present theory one can derive some overpenalized IP bilinear forms avoiding the notion of fluxes and artificial penalty terms. The main idea is to start from bilinear forms for the local average of discontinuous approximatio...

A posteriori $ L^2(L^2)$-error estimates with the new version of streamline diffusion method for the wave equation

In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori $ L^2(L^2)$ and error estimates for this method under minimal regularity hypothesis. Test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

Analysis of a posteriori error estimates of the discontinuous Galerkin method for nonlinear ordinary differential equations

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