Abdulle, AssyrHuber, Martin Ernst2014-08-222014-08-222014-08-22201610.1002/num.22037https://infoscience.epfl.ch/handle/20.500.14299/105996WOS:000373722900011We consider a finite element method (FEM) with arbitrary polynomial degree for nonlinear monotone elliptic problems. Using a linear elliptic projection, we first give a new short proof of the optimal convergence rate of the FEM in the L2 norm. We then derive optimal a priori error estimates in the H 1 and L2 norm for a FEM with variational crimes due to numerical integration. As an application we derive a priori error estimates for a numerical homogenization method applied to nonlinear monotone elliptic problems.Nonlinear monotone elliptic problemhigh order finite element methodelliptic projectionnumerical integrationvariational crimesnumerical homogenization.text::journal::journal article::research article