Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization

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 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.


Published in:
Numerical Methods for Partial Differential Equations, 32, 3, 955-969
Year:
2016
Publisher:
Hoboken, Wiley-Blackwell
ISSN:
0749-159X
Keywords:
Laboratories:




 Record created 2014-08-22, last modified 2018-03-17

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