## On a variant of the local projection method stable in the SUPG norm

- ID: 2471, RIV: 10026758
- ISSN: 0023-5954, ISBN: not specified
- source: Kybernetika
- keywords: variant; local; projection; method; stable; norm
- authors: Petr Knobloch
- authors from KNM: Knobloch Petr

### Abstract

We consider the local projection finite element method for the discretization of a scalar convection-diffusion equation with a divergence-free convection field. We introduce a new fluctuation operator which is defined using an orthogonal L2 projection with respect to a weighted L2 inner product. We prove that the bilinear form corresponding to the discrete problem satisfies an inf-sup condition with respect to the SUPG norm and derive an error estimate for the discrete solution.