Visualization of higher order finite elements.

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Description

Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there ... continued below

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46 p.

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Thompson, David C.; Pebay, Philippe Pierre; Crawford, Richard H. & Khardekar, Rahul Vinay April 1, 2004.

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Description

Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there are curved boundaries on the problem domain, {Omega}, it becomes algorithmically much more difficult to define {Phi} in terms of x. Rather, we define an archetypal element in a new coordinate space, r = ( r s t ), which has a simple, axis-aligned boundary (see Figure 1(b)) and place two maps onto our archetypal element:

Physical Description

46 p.

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  • Report No.: SAND2004-1617
  • Grant Number: AC04-94AL85000
  • DOI: 10.2172/919127 | External Link
  • Office of Scientific & Technical Information Report Number: 919127
  • Archival Resource Key: ark:/67531/metadc879244

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  • April 1, 2004

Added to The UNT Digital Library

  • Sept. 22, 2016, 2:13 a.m.

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  • Dec. 2, 2016, 6:15 p.m.

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Thompson, David C.; Pebay, Philippe Pierre; Crawford, Richard H. & Khardekar, Rahul Vinay. Visualization of higher order finite elements., report, April 1, 2004; United States. (digital.library.unt.edu/ark:/67531/metadc879244/: accessed September 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.