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On the application of local projection methods to convection-diffusion-reaction problems. (English) Zbl 1180.35051

Hegarty, Alan F. (ed.) et al., BAIL 2008 – Boundary and interior layers. Proceedings of the international conference on boundary and interior layers – computational and asymptotic methods, Limerick, Ireland, July 28–August 1, 2008. Berlin: Springer (ISBN 978-3-642-00604-3/pbk; 978-3-642-00605-0/ebook). Lecture Notes in Computational Science and Engineering 69, 183-194 (2009).
Summary: We apply the local projection stabilization to finite element discretizations of scalar convection-diffusion-reaction equations with mixed boundary conditions. We derive general error estimates and discuss the choice of the stabilization parameter. Numerical results illustrate some drawbacks of the local projection stabilization in comparison to the SUPG method.
For the entire collection see [Zbl 1167.35002].

MSC:

35B25 Singular perturbations in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
35A35 Theoretical approximation in context of PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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