Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization |
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| Authors: | Assyr Abdulle Martin E Huber |
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| Affiliation: | ANMC, Mathematics Section, école Polytechnique Fédérale de Lausanne, Lausanne, Switzerland |
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| Abstract: | 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 H1 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. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 955–969, 2016 |
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| Keywords: | elliptic projection high order finite element method nonlinear monotone elliptic problem numerical homogenization numerical integration variational crimes |
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