The functions φ1, φ2,…, φn are always chosen to be simple and are called trial functions. The success of the method is due in part to choosing these functions to be low-degree splines. This in turn generally leads to a system of equations for the coefficients c1, c2,…, cn that involves the treatment of sparse matrices, i.e. matrices in which a large proportion of the elements are zero; very efficient software can then be used.
In Galerkin's method the criterion for choosing the coefficients is that the amount by which u(x) fails to satisfy the equation is in a certain sense small. The Rayleigh–Ritz method is a variational method. The finite-element method can in general be regarded as a process in which a solution in an infinite-dimensional space is replaced by an approximation that lies in a finite-dimensional subspace. The whole process is referred to as finite-element analysis.
"finite-element method." A Dictionary of Computing. . Encyclopedia.com. (March 20, 2019). https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/finite-element-method
"finite-element method." A Dictionary of Computing. . Retrieved March 20, 2019 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/finite-element-method
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.