Journal
COMPUTATIONAL GEOSCIENCES
Volume 23, Issue 1, Pages 189-199Publisher
SPRINGER
DOI: 10.1007/s10596-018-9792-y
Keywords
Darcy equation; Fracture; Embedded layer; Cut finite element methods
Funding
- Swedish Foundation for Strategic Research [AM13-0029]
- Swedish Research Council [2011-4992, 2013-4708]
- Swedish Research Programme Essence
- EPSRC [EP/P01576X/1]
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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.
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