Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization
نویسندگان
چکیده
We 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 L norm. We then derive optimal a priori error estimates in the H and L 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.
منابع مشابه
The effect of numerical integration in nonmonotone nonlinear elliptic problems with application to numerical homogenization methods
A finite element method with numerical quadrature is considered for the solution of a class of second-order quasilinear elliptic problems of nonmonotone type. Optimal a priori error estimates for the H and the L norms are derived. The uniqueness of the finite element solution is established for a sufficiently fine mesh. Application to numerical homogenization methods is considered.
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