Skip to main content

Patchwork Approximation in Numerical Analysis

  • Chapter
Rational Bases and Generalized Barycentrics
  • 740 Accesses

Abstract

The numerical solution to a problem is often expressed in terms of an approximation \(\mathrm{U(\underline{x})}\) to the true solution \(\mathrm{u(\underline{x})\mbox{ for }\underline{x}}\) in some prescribed region D.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • M. Bocher, Introduction to Higher Algebra (MacMillan, New York, 1907)

    MATH  Google Scholar 

  • P.G. Ciarlet, P.A. Raviart, Interpolation theory over curved elements, with applications to finite element methods, in Computer Methods in Applied Mechanics and Engineering (North-Holland, Amsterdam, 1972a), pp. 217–249

    Google Scholar 

  • J. Ergatoudis, Quadrilateral elements in plane analysis. Masters thesis, University of Wales, Swansea, 1966

    Google Scholar 

  • B.M. Irons, Numerical integration applied to finite element methods, in Conf. on use of Digital Computers in Structural Eng., University of Newcastle, 1966

    Google Scholar 

  • W.B. Jordan, Plane isoparametric structural element, KAPL Memo M-7112, UC-32, in Mathematics and Computers TID-4500, 54th edn. (1970)

    Google Scholar 

  • A.R. Mitchell, G. Phillips, E.L. Wachspress, Forbidden elements in the finite element method. J. Inst. Math. Appl. 8, 260–269 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  • G. Strang, G.J. Fix, An Analysis of the Finite Element Method (Prentice Hall, Englewood Cliffs, 1973)

    MATH  Google Scholar 

  • J.L. Synge, The Hypercircle in Mathematical Physics (Cambridge University Press, Cambridge, 1957)

    MATH  Google Scholar 

  • R. Wait, A finite element for three dimensional function approximation, in Proc. Conf. on Appl. Numerical Anal., Dundee. Lecture Notes in Mathematics, vol. 228 (Springer, New York, 1971), pp. 348–352

    Google Scholar 

  • R. Walker, Algebraic Curves (Dover, New York, 1962)

    MATH  Google Scholar 

  • O.C. Zienkiewicz, The Finite Element Method in Engineering Science, 2nd edn. (McGraw Hill, New York, 1971)

    MATH  Google Scholar 

  • O.C. Zienkiewicz, Y.K. Cheung, Finite Element Methods in Structural Mechanics (McGraw Hill, New York, 1967)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Wachspress, E. (2016). Patchwork Approximation in Numerical Analysis. In: Rational Bases and Generalized Barycentrics. Springer, Cham. https://doi.org/10.1007/978-3-319-21614-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21614-0_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21613-3

  • Online ISBN: 978-3-319-21614-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics