TY - JOUR
T1 - Error Estimates in Balanced Norms of Finite Element Methods for Higher Order Reaction-Diffusion Problems
AU - Franz , Sebastian
AU - Roos , Hans-G.
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 532
EP - 542
PY - 2020
DA - 2020/08
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/17868.html
KW - Balanced norms, reaction-diffusion problems, finite element methods.
AB - <p style="text-align: justify;">Error estimates of finite element methods for reaction-diffusion problems are often
realised in the related energy norm. In the singularly perturbed case, however, this norm is not
adequate. A different scaling of the $H$<sup>$m$</sup>&nbsp;seminorm for 2$m$-th order problems leads to a balanced
norm which reflects the layer behaviour correctly. We prove error estimates in such balanced
norms and improve thereby existing estimates known in literature.</p>