A study of some new inequalities for Galerkin method for model diffusion problem and finite element basis

Abstract

Our work is concerned with the Galerkin projection method for the numerical solution of partial differential equations (PDEs). In particular, those which include polynomial basis function and finite element basis. Polynomial basis function should be avoided and the reason behind that is presented. Also, we will see that the Galerkin method plays an important role in integrals of functions that can easily be evaluated on the domain. In addition, the Galerkin method presents a high-order approximation. Smart problems are presented for clarification and signification on their properties, and proof of some tricky inequalities