UNIFORM A PRIORI ESTIMATES FOR SINGULARLY PERTURBED ELLIPTIC EQUATIONS IN MULTIDIMENSIONS

@inproceedings{Numer1999UNIFORMAP,
  title={UNIFORM A PRIORI ESTIMATES FOR SINGULARLY PERTURBED ELLIPTIC EQUATIONS IN MULTIDIMENSIONS},
  author={Siam J. Numer},
  year={1999}
}
We consider a linear singularly perturbed elliptic equation on a bounded domain in R n . This equation serves as a model for the interplay between the transport term and a relatively small viscosity term in some problems of mathematical physics. We establish a priori estimates that hold uniformly in the small parameter. From this one can prove an abstract a priori error estimate for the discretization with conforming nite elements. For globally directed transport elds we establish a new type of… CONTINUE READING

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