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Remarks on balanced norm error estimates for systems of reaction-diffusion equations
Applications of Mathematics, Tome 63 (2018) no. 3, pp. 273-279 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the $H^1$ seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss the difficulties which arise for systems of reaction-diffusion problems.
Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the $H^1$ seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss the difficulties which arise for systems of reaction-diffusion problems.
DOI : 10.21136/AM.2018.0063-18
Classification : 65N30
Keywords: singular perturbation; finite element method; layer-adapted mesh; balanced norm 
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     title = {Remarks on balanced norm error estimates for systems of reaction-diffusion equations},
     journal = {Applications of Mathematics},
     pages = {273--279},
     year = {2018},
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Roos, Hans-Goerg. Remarks on balanced norm error estimates for systems of reaction-diffusion equations. Applications of Mathematics, Tome 63 (2018) no. 3, pp. 273-279. doi: 10.21136/AM.2018.0063-18

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