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A simple finite element method for elliptic bulk problems with embedded surfaces
Department of Mathematics, University College London, London, United Kingdom.
Jönköping University, School of Engineering, JTH, Materials and Manufacturing.ORCID iD: 0000-0001-7352-1550
Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden.
2019 (English)In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499, Vol. 23, no 1, p. 189-199Article in journal (Refereed) Published
Abstract [en]

In this paper, we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the mesh in arbitrary fashion and we take the flow in the crack into account by superposition. The fact that we use continuous elements leads to suboptimal convergence due to the loss of regularity across the crack. We therefore refine the mesh in the vicinity of the crack in order to recover optimal order convergence in terms of the global mesh parameter. The proper degree of refinement is determined based on an a priori error estimate and can thus be performed before the actual finite element computation is started. Numerical examples showing this effect and confirming the theoretical results are provided. The approach is easy to implement and beneficial for rapid assessment of the effect of crack orientation and may for example be used in an optimization loop. 

Place, publisher, year, edition, pages
Springer, 2019. Vol. 23, no 1, p. 189-199
Keywords [en]
Cut finite element methods, Darcy equation, Embedded layer, Fracture
National Category
Computer Engineering
Identifiers
URN: urn:nbn:se:hj:diva-42144DOI: 10.1007/s10596-018-9792-yISI: 000459423400010Scopus ID: 2-s2.0-85056316370Local ID: HOA JTH 2019;JTHProduktutvecklingISOAI: oai:DiVA.org:hj-42144DiVA, id: diva2:1265933
Available from: 2018-11-26 Created: 2018-11-26 Last updated: 2019-03-14Bibliographically approved

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Hansbo, Peter

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