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Linear finite elements may be only first-order pointwise accurate on antisotropic triangulations
Date
2014
Abstract
We give a counterexample of an anisotropic triangulation on which the exact solution has a second-order error of linear interpolation, while the computed solution obtained using linear finite elements is only first-order pointwise accurate. Our example is given in the context of a singularly perturbed reaction-diffusion equation, whose exact solution exhibits a sharp boundary layer. Furthermore, we give a theoretical justification of the observed numerical phenomena using a finite-difference representation of the considered finite element methods. Both standard and lumped-mass cases are addressed.
Supervisor
Description
peer-reviewed
Publisher
American Mathematical Society
Citation
Mathematics of Computation;83, 289, pp. 2061-2070
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kopteva_mc2012_R1.pdf
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