A posteriori error estimates of Darcy flows with Robin-type jump interface conditions
Numerical Analysis
2024-12-17 v2 Numerical Analysis
Abstract
In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg post-processing. The reliability of the estimator is proved using an interface-adapted Helmholtz-type decomposition and an interface-adapted Scott--Zhang type interpolation operator. A local efficiency and the reliability of post-processed pressure are also proved. Numerical results illustrating adaptivity algorithms using our estimator are included.
Keywords
Cite
@article{arxiv.2304.14287,
title = {A posteriori error estimates of Darcy flows with Robin-type jump interface conditions},
author = {Jeonghun J. Lee},
journal= {arXiv preprint arXiv:2304.14287},
year = {2024}
}