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Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems

Date
2016
Abstract
Residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polyhedral domains. Standard finite element approximations are considered. The error constants are independent of the diameters of mesh elements and the small perturbation parameter. In our analysis, we employ sharp bounds on the Green's function of the linearized differential operator. Numerical results are presented that support our theoretical findings.
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Description
peer-reviewed
Publisher
Springer
Citation
Numerische Mathematik;133 (4), pp. 707-742
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Mathematics & Statistics
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demlow_kopteva_NM.pdf
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Keywords
a posteriori error estimate, maximum norm, singular perturbation
ULRR Identifiers
https://hdl.handle.net/10344/5775
 https://doi.org/10.34961/4160
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Funding Information
Science Foundation Ireland (SFI)
Sustainable Development Goals
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