A-Posteriori Error Estimates for Uniform $p$-Version Finite Element Methods in Square

Abstract

In this work, the $a$-$posteriori$ error indicator with an explicit formula for $p$-version finite element methods in square is investigated, and its reliable and efficient properties are deduced. Especially, this $a$-$posteriori$ error indicator is determined by the right hand item of the model. We reformulate this $a$-$posteriori$ error indicator with finite coefficients, which can be easily calculated during applications.