Quasi - Optimal Estimates for Finite Element Approximations Using Orlicz Norms
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چکیده
We consider the approximation by linear finite elements of the solution of the Dirichlet problem -Au = /. We obtain a relation between the error in the infinite norm and the error in some Orlicz spaces. As a consequence, we get quasi-optimal uniform estimates when u has second derivatives in the Orlicz space associated with the exponential function. This estimate contains, in particular, the case where / belongs to L00 and the boundary of the domain is regular. We also show that optimal order estimates are valid for the error in this Orlicz space provided that u be regular enough.
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تاریخ انتشار 2010