An interior-penalty discontinuous Galerkin (dG) method for an elliptic interface problem involving, possibly, curved interfaces, with fluxbalancing interface conditions, e.g., modelling mass transfer of solutes through semi-permeable membranes, is considered. The method allows for extremely general curved element shapes employed to resolve the interface geometry exactly. A residual-type a posteriori error estimator for this dG method is proposed and upper and lower bounds of the error in the respective dG-energy norm are proven. The a posteriori error bounds are subsequently used to prove a basic a priori convergence result. The theory presented is complemented by a series of numerical experiments. The presented approach applies immediately to the case of curved domains with non-essential boundary conditions, too.

Adaptive discontinuous Galerkin methods for elliptic interface problems / Cangiani, A.; Georgoulis, E. H.; Sabawi, Y. A.. - In: MATHEMATICS OF COMPUTATION. - ISSN 1088-6842. - 87:314(2018), pp. 2675-2707. [10.1090/mcom/3322]

Adaptive discontinuous Galerkin methods for elliptic interface problems

Cangiani A.;
2018-01-01

Abstract

An interior-penalty discontinuous Galerkin (dG) method for an elliptic interface problem involving, possibly, curved interfaces, with fluxbalancing interface conditions, e.g., modelling mass transfer of solutes through semi-permeable membranes, is considered. The method allows for extremely general curved element shapes employed to resolve the interface geometry exactly. A residual-type a posteriori error estimator for this dG method is proposed and upper and lower bounds of the error in the respective dG-energy norm are proven. The a posteriori error bounds are subsequently used to prove a basic a priori convergence result. The theory presented is complemented by a series of numerical experiments. The presented approach applies immediately to the case of curved domains with non-essential boundary conditions, too.
2018
87
314
2675
2707
Cangiani, A.; Georgoulis, E. H.; Sabawi, Y. A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/135257
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