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Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
Abstract
In this paper the approximate solution of a class of second order elliptic equations with rough coefficients is considered. Problems of the type considered arise in the analysis of unidirectional composites, where the coefficients represent the properties of the material. Several methods for this class of problems are presented, and it is shown that they have the same accuracy as usual methods have for problems with smooth coefficients. The methods are referred to as special finite element methods because they are of finite element type but employ special shape functions, chosen to accurately model the unknown solution.
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Cited by
Multi-level partition of unity implicits
Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., & Seidel, H.-P. (2005) · ACM SIGGRAPH 2005 Courses on - SIGGRAPH '05 · doi:10.1145/1198555.1198649 · Cited by 722
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“Partitions of unity are of course not new, see, e.g. [Babuška et al. 1994; Ohtake et al. 2003]; our contribution is to combine them with neural networks and a multi-resolution scheme.”
Metadata
- Authors
- Babuška, I., Caloz, G., & Osborn, J. E.
- Venue
- SIAM Journal on Numerical Analysis
- Published
- 1994-08
- Volume
- 31
- Issue
- 4
- Pages
- 945-981
- ISSN
- 0036-1429 (ISSN-L)
- 1095-7170
- OpenAlex
- W2157721313
- Cited by
- 661
- References
- 0
- FWCI
- 4.66
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients. https://app.cochat.ai/papers/10.1137/0731051
- The paper
- Babuška, I., Caloz, G., & Osborn, J. E. (1994). Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients. SIAM Journal on Numerical Analysis. https://doi.org/10.1137/0731051
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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