Robust A Posteriori Error Estimates for Nonstationary Convection-Diffusion Equations

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.

A posteriori error estimates for linear parabolic equations

We consider discretizations of linear parabolic equations by A-stable θ-schemes in time and conforming finite elements in space. For these discretizations we derive a residual a posteriori error estimator. The estimator yields upper bounds on the error which are global in space and time and lower bounds that are global in space and local in time. The error estimates are fully robust in the sens...

A posteriori error estimate for finite volume approximations of nonlinear heat equations

In this contribution we derive a posteriori error estimate for finite volume approximations of nonlinear convection diffusion equations in the L∞(L1)-norm. The problem is discretized implicitly in time by the method of characteristics, and in space by piecewise constant finite volume methods. The analysis is based on a reformulation for finite volume methods. The derived a posteriori error esti...

A Posteriori Error Estimates for Vertex Centered Finite Volume Approximations of Convection-diffusion-reaction Equations

This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation ct+∇·(uf(c))−∇·(D∇c)+λc = 0. The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L-norm, independent of the diffusion parameter D. The resulting a posteriori error estimate is used to de...

A Posteriori Error Estimates for Finite Volume Element Approximations of Convection-diffusion-reaction Equations