@Article{AAM-39-2,
author = {Yan, Chen and Ruo, Li and Qicheng, Liu},
title = {An Arbitrary Order Reconstructed Discontinuous Approximation to Biharmonic Interface Problem},
journal = {Annals of Applied Mathematics},
year = {2023},
volume = {39},
number = {2},
pages = {149--180},
abstract = {<p style="text-align: justify;">We present an arbitrary order discontinuous Galerkin finite element
method for solving the biharmonic interface problem on the unfitted mesh. The
approximation space is constructed by a patch reconstruction process with at
most one degrees of freedom per element. The discrete problem is based on
the symmetric interior penalty method and the jump conditions are weakly
imposed by the Nitsche’s technique. The $C^2$-smooth interface is allowed to
intersect elements in a very general fashion and the stability near the interface
is naturally ensured by the patch reconstruction. We prove the optimal a priori
error estimate under the energy norm and the $L^2$ norm. Numerical results are
provided to verify the theoretical analysis.</p>},
issn = {},
doi = {https://doi.org/10.4208/aam.OA-2023-0011},
url = {https://global-sci.com/article/72609/an-arbitrary-order-reconstructed-discontinuous-approximation-to-biharmonic-interface-problem}
}