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$$L^{2}(H^{1})$$ norm a posteriori error estimation for discontinuous Galerkin approximations of reactive transport problems. (English) Zbl 1066.76037
Summary: Explicit a posteriori residual type error estimators in $$L^{2}(H^{1})$$ norm are derived for discontinuous Galerkin (DG) methods applied to transport in porous media with general kinetic reactions. They are flexible and apply to all the four primal DG schemes, namely, Oden-Babuška-Baumann DG method, non-symmetric interior penalty Galerkin method, symmetric interior penalty Galerkin and incomplete interior penalty Galerkin method. The error estimators use directly all the available information from the numerical solution and can be computed efficiently. Numerical examples demonstrate the efficiency of these theoretical estimators.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 76V05 Reaction effects in flows 76S05 Flows in porous media; filtration; seepage 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
##### Keywords:
Oden-Babuška-Baumann method; penalty method
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##### References:
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