This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation ${c}_{t}+\nabla \xb7\left(\mathbf{u}f\left(c\right)\right)-\nabla \xb7\left(D\nabla c\right)+\lambda c=0$. The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the ${L}^{1}$-norm, independent of the diffusion parameter $D$. The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability...

This paper is devoted to the study of
error estimates for the scalar nonlinear convection-diffusion-reaction equation
${c}_{t}+\nabla \xb7\left(\mathbf{u}f\left(c\right)\right)-\nabla \xb7\left(D\nabla c\right)+\lambda c=0$.
The estimates for the error between the exact solution and an upwind finite
volume approximation to the solution are derived in the
-norm,
independent of the diffusion parameter .
The resulting error estimate is used to define an grid adaptive solution
algorithm for the finite volume scheme. Finally numerical experiments underline
the applicability of...

The model order reduction methodology of
techniques offers efficient treatment of parametrized partial differential
equations (PDEs) by providing both approximate solution procedures and
efficient error estimates.
RB-methods have so far mainly been applied to finite element schemes
for elliptic and parabolic problems. In the current study
we extend the methodology to general linear evolution schemes such as finite volume schemes for parabolic and hyperbolic evolution equations. The new theoretic...

Download Results (CSV)