NDLI: A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems

Content Provider	Springer Nature Link
Author	Stynes, Martin Lin, Runchang
Copyright Year	2015
Abstract	A system of linear coupled reaction-diffusion equations is considered, where each equation is a two-point boundary value problem and all equations share the same small diffusion coefficient. A finite element method using piecewise quadratic splines that are globally C $^{1}$ is introduced; its novelty lies in the norm associated with the method, which is stronger than the usual energy norm and is “balanced”, i.e., each term in the norm is O(1) when the norm is applied to the true solution of the system. On a standard Shishkin mesh with N subintervals, it is shown that the method is $O(N^{-1}\ln N)$ accurate in the balanced norm. Numerical results to illustrate this result are presented.
Ending Page	707
Page Count	17
Starting Page	691
File Format	PDF
ISSN	10171398
e-ISSN	15729265
Journal	Numerical Algorithms
Issue Number	4
Volume Number	70
Language	English
Publisher	Springer US
Publisher Date	2015-02-04
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Boundary value problems Singular perturbation Spline interpolant Balanced norm Numeric Computing Theory of Computation Shishkin mesh Algorithms Algebra Finite elements, Rayleigh-Ritz, Galerkin and collocation methods Numerical Analysis Reaction-diffusion Mesh generation and refinement Error bounds
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems