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 . 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 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