Reconstruction based a posteriori error estimators for the transport equation

Roland Becker (1, 2) , Daniela Capatina (1, 2) , Robert Luce (1, 2)

1 CONCHA - Complex Flow Simulation Codes based on High-order and Adaptive methods
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We present a unified approach to build error estimators based on H(div)-reconstructed fluxes on the primal mesh, inspired by the hypercircle method. Here, the transport equation is considered and discretized by discontinuous Galerkin, nonconforming and conforming finite elements. We describe the local computation of fluxes on patches, obtain upper error bounds and show some numerical tests.

Domaines: Analyse numérique [math.NA]

Roland Becker, Daniela Capatina, Robert Luce. Reconstruction based a posteriori error estimators for the transport equation. Numerical Mathematics and Advanced Applications 2011, Springer, pp.13-21, 2013, 978-3-642-33133-6. ⟨10.1007/978-3-642-33134-3_2⟩. ⟨hal-00868463⟩