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On the stability of finite-element discretizations of convection-diffusion-reaction equations. (English) Zbl 1211.65147

The paper deals with the numerical solution of convection-diffusion-reaction equations with the aid of finite element methods. The scheme is stabilized by local projection (LP). An a priori error analysis of LP is generally based on the coercivity of the underlying bilinear form with respect to the LP norm. The authors show that the bilinear form of the LP stabilization satisfies an inf-sup condition in a stronger norm that is equivalent to that of the streamline upwind/Petrov-Galerkin method. As a consequence, they get some insight into the stabilization mechanism of Galerkin discretizations of higher order. Numerical experiments are included.

MSC:

65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N15 Error bounds for boundary value problems involving PDEs
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