TY - JOUR
T1 - Error Splitting Preservation for High Order Finite Difference Schemes in the Combination Technique
AU - Christian Hendricks, Matthias Ehrhardt & Michael Günther
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 689
EP - 710
PY - 2017
DA - 2017/10
SN - 10
DO - http://doi.org/10.4208/nmtma.2017.m1511
UR - https://global-sci.org/intro/article_detail/nmtma/12365.html
KW - 
AB - <p style="text-align: justify;">In this paper we introduce high dimensional tensor product interpolation for the combination technique. In order to compute the sparse grid solution, the
discrete numerical subsolutions have to be extended by interpolation. If unsuitable interpolation techniques are used, the rate of convergence is deteriorated.
We derive the necessary framework to preserve the error structure of high order finite difference solutions of elliptic partial differential equations within the combination technique framework.
This strategy enables us to obtain high order sparse grid solutions on the full grid. As exemplifications for the case of order four we illustrate our theoretical results
by two test examples with up to four dimensions.</p>