@inbook{88b8d64c9f274af3a9ecb496f636d0fc,
title = "An implicit gradient meshfree formulation for convection-dominated problems",
abstract = "Meshfree approximations are ideal for the gradient-type stabilized Petrov-Galerkin methods used for solving Eulerian conservation laws due to their ability to achieve arbitrary smoothness,however,the gradient terms are computationally demanding for meshfree methods. To address this issue,a stabilization technique that avoids high order differentiation of meshfree shape functions is introduced by employing implicit gradients under the reproducing kernel approximation framework. The modification to the standard approximation introduces virtually no additional computational cost,and its implementation is simple. The effectiveness of the proposed method is demonstrated in several benchmark problems.",
author = "M. Hillman and Chen, {J. S.}",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.",
year = "2016",
doi = "10.1007/978-3-319-40827-9_3",
language = "English (US)",
series = "Modeling and Simulation in Science, Engineering and Technology",
publisher = "Springer Basel",
pages = "25--37",
booktitle = "Modeling and Simulation in Science, Engineering and Technology",
}