Technical note: Finite element formulations to map discrete fracture elements in three-dimensional groundwater models
<p>Typically, in finite element groundwater models, fractures are represented by two-dimensional triangular or quadrilateral elements. When embedded in a three-dimensional space, the Jacobian matrix governing the transformation from the global three-dimensional space to the local two-dimension...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2025-06-01
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| Series: | Hydrology and Earth System Sciences |
| Online Access: | https://hess.copernicus.org/articles/29/2697/2025/hess-29-2697-2025.pdf |
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| Summary: | <p>Typically, in finite element groundwater models, fractures are represented by two-dimensional triangular or quadrilateral elements. When embedded in a three-dimensional space, the Jacobian matrix governing the transformation from the global three-dimensional space to the local two-dimensional space is rectangular and thus not invertible. There exist different approaches to obtain a unique mapping from local to global space even though the Jacobian matrix is not invertible. These approaches are discussed in this study. It is illustrated that all approaches yield the same result and may be applied to curved elements. The mapping of anisotropic hydraulic conductivity tensors for possibly curved fracture elements is also discussed.</p> |
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| ISSN: | 1027-5606 1607-7938 |