Recovery-type Posteriori Error Estimate For The Conduction Convection Problem

Finite element error analysis and quantization have always been one of the important problems in finite element theory analysis and calculation.And the numerical calculation workers hope to quantity the error of the finite element approximation solution with the least cost.The finite element posteriori error estimate and adaptive algorithm arise to control the solution in certain precision.In the finite element numerical calculation,we often encounter a numerical approximation of the overall accuracy decline gradually for the local singularity,such as boundary layer,fault layer,corner and etc.The measures which easy to think of is refinement in these critical areas.The finite element a posterior error used the finite element priori to construct the error estimator,and the posterior error estimator can be indicated the area that needs to be processed and followed by a grid of local encryption.According to the principle of the structure of estimator,the adaptive finite element method can be divided into the residual error estimator and the recovery error estimator generally.The residual error estimate is based on the residual equation.It is known that the selection of residual equation is different,and the definition of residual equation is the principal method of the construction estimator in the posterior error.The recovery a posterior error estimate increase the partial fraction to a higher degree of fitting,because of the recovery method is simple and easy coding so it is more suitable for industrial application.Based on the work of predecessors,this paper constructs the recovery estimator of the conduction convection equation based on the technique of gradient reconstruction and superconvergence,the class of estimator is not dependent on the original equation,but only with the numerical solution.