Abstract
We establish an error estimate for fully discrete time-space gradient schemes on a simple linear parabolic equation. This error estimate holds for all the schemes within the framework of the gradient discretisation method: conforming and non conforming finite element, mixed finite element, hybrid mixed mimetic family, some Multi-Point Flux approximation finite volume scheme and some discontinuous Galerkin schemes.
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Acknowledgements
We thank the Australian Research Council’s Discovery Projects funding scheme (project number DP170100605) for partially supporting this work.
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Droniou, J., Eymard, R., Gallouët, T., Guichard, C., Herbin, R. (2017). An Error Estimate for the Approximation of Linear Parabolic Equations by the Gradient Discretization Method. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_30
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DOI: https://doi.org/10.1007/978-3-319-57397-7_30
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