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6997 results in Mathematical modeling and methods

Page 23 of 350

  • A MODIFIED IMMERSED FINITE VOLUME ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS

  • Part of
  • Q. WANG, Z. ZHANG
  • Journal:
    The ANZIAM Journal / Volume 62 / Issue 1 / January 2020
    Published online by Cambridge University Press:
    13 May 2020, pp. 42-61
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  • This paper presents a new immersed finite volume element method for solving second-order elliptic problems with discontinuous diffusion coefficient on a Cartesian mesh. The new method possesses the local conservation property of classic finite volume element method, and it can overcome the oscillating behaviour of the classic immersed finite volume element method. The idea of this method is to reconstruct the control volume according to the interface, which makes it easy to implement. Optimal error estimates can be derived with respect to an energy norm under piecewise $H^{2}$ regularity. Numerical results show that the new method significantly outperforms the classic immersed finite volume element method, and has second-order convergence in $L^{\infty }$ norm.

Essential Mathematics for Engineers and Scientists
  • Thomas J. Pence, Indrek S. Wichman
  • Published online:
    30 April 2020
    Print publication:
    21 May 2020
  • This text is geared toward students who have an undergraduate degree or extensive coursework in engineering or the physical sciences and who wish to develop their understanding of the essential topics of applied mathematics. The methods covered in the chapters form the core of analysis in engineering and the physical sciences. Readers will learn the solutions, techniques, and approaches that they will use as academic researchers or industrial R&D specialists. For example, they will be able to understand the fundamentals behind the various scientific software packages that are used to solve technical problems (such as the equations describing the solid mechanics of complex structures or the fluid mechanics of short-term weather prediction and long-term climate change), which is crucial to working with such codes successfully. Detailed and numerous worked problems help to ensure a clear and well-paced introduction to applied mathematics. Computational challenge problems at the end of each chapter provide students with the opportunity for hands-on learning and help to ensure mastery of the concepts. Adaptable to one- and two-semester courses.

  • ANZ VOLUME 61 ISSUE 4 COVER AND BACK MATTER

  • Journal:
    The ANZIAM Journal / Volume 61 / Issue 4 / October 2019
    Published online by Cambridge University Press:
    24 April 2020, pp. b1-b9
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  • ANZ VOLUME 61 ISSUE 4 COVER AND FRONT MATTER

  • Journal:
    The ANZIAM Journal / Volume 61 / Issue 4 / October 2019
    Published online by Cambridge University Press:
    24 April 2020, pp. f1-f2
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Page 23 of 350