Maximum Norm Estimates for Energy-Corrected Finite Element Method
Nonsmoothness of the boundary of polygonal domains limits the regularity of the solutions of elliptic problems. This leads to the presence of the so-called pollution effect in the finite element approximation, which results in a reduced convergence order of the scheme measured in the L2 and L∞-norms, compared to the best-approximation order. We show that the energy-correction method, which is known to eliminate the pollution effect in the L2-norm, yields the same convergence order of the finite element error as the best approximation also in the L∞-norm. We confirm the theoretical results with numerical experiments.
We gratefully acknowledge the support of the German Research Foundation (DFG) through the grant WO 671/11-1 and, together with the Austrian Science Fund, through the IGDK1754 Training Group. We would also like to thank Dr Johannes Pfefferer for many fruitful and helpful discussions.
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