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A posteriori error estimation for interior penalty finite element approximations of the advection-reaction equation. (English) Zbl 1205.65249

This note considers residual-based a posteriori error estimation for finite element approximations of the transport equation. For discretization it uses piecewise affine continuous or discontinuous finite elements and symmetric stabilization of interior penalty type. The lowest order discontinuous Galerkin method using piecewise constant approximation is included as a special case. The key elements in the analysis are a saturation assumption and an approximation result for interpolation between discrete spaces.

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L04 Initial-boundary value problems for first-order hyperbolic equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

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