Quasi-optimal estimates for finite element approximations using Orlicz norms

Durán, Ricardo G.

doi:10.1090/S0025-5718-1987-0890251-6

Quasi-optimal estimates for finite element approximations using Orlicz norms
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by Ricardo G. Durán PDF

Math. Comp. 49 (1987), 17-23 Request permission

Abstract:

We consider the approximation by linear finite elements of the solution of the Dirichlet problem $- \Delta u = f$. 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 f belongs to ${L^\infty }$ 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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