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Mathematics of Computation

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Quasi-optimal estimates for finite element approximations using Orlicz norms


Author: Ricardo G. Durán
Journal: Math. Comp. 49 (1987), 17-23
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1987-0890251-6
MathSciNet review: 890251
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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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DOI: https://doi.org/10.1090/S0025-5718-1987-0890251-6
Article copyright: © Copyright 1987 American Mathematical Society