Abstract
A two-point flux approximation (TPFA) finite volume method is considered for mixed-dimensional fracture flow problems. Its construction is based on applying a face-based quadrature rule to a conforming, mixed finite element scheme of lowest order. A concise argument shows linear convergence in theory, which we confirm in practice by a numerical experiment.
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Boon, W.M., Nordbotten, J.M. (2020). Convergence of a TPFA Finite Volume Scheme for Mixed-Dimensional Flow Problems. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_40
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DOI: https://doi.org/10.1007/978-3-030-43651-3_40
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