An a Posteriori Error Estimate for Finite Volume Methods: Parabolic Problems

Abstract. An a posteriori error estimate for finite volume methods in triangular meshes is developed and successfully implemented for parabolic heat transfer problems. The proposed error estimate belongs to the class of truncation-error estimates. A polynomial function was successfully employed in the estimation of the solution used in the error formulation. A simple and reliable h-type adaptive methodology was also developed and successfully implemented. The major feature of the adaptive methodology consists on the fact that the proposed error estimate does not require the solution of systems of equations as in the case of estimates belonging to other classes. The error differences using analytical and estimate solutions were compared for three parabolic heat transfer problems, and a good performance of the adaptive procedure was verified.