@article{b38d5ee5f03745bbbb70609726a2ed4e,
title = "A primal-dual weak galerkin finite element method for fokker planck type equations",
abstract = "This paper presents a primal-dual weak Galerkin finite element method for a class of second order elliptic equations of Fokker-Planck type. The method is based on a variational form where all the derivatives are applied to the test functions so that no regularity is necessary for the exact solution of the model equation. The numerical scheme is designed by using locally constructed weak second order partial derivatives and the weak gradient commonly used in the weak Galerkin context. Optimal order of convergence is derived for the resulting numerical solutions. Numerical results are reported to demonstrate the performance of the numerical scheme.",
keywords = "Finite element methods, Fokker-Planck equation, Polytopal partitions, Primal-dual, Weak Galerkin, Weak Hessian, Weak gradient",
author = "Chunmei Wang and Junping Wang",
note = "Funding Information: \ast Received by the editors April 21, 2017; accepted for publication (in revised form) April 24, 2018; published electronically September 23, 2020. https://doi.org/10.1137/17M1126618 Funding: The work of the first author was partially supported by National Science Foundation Award DMS-1849483. The work of the second author was supported by the NSF IR/D program, while working at National Science Foundation. However, any opinion, finding, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. \dagger Department of Mathematics, Texas Tech University, Lubbock, TX 79409 (chunmei. wang@ttu.edu). \ddagger Division of Mathematical Sciences, National Science Foundation, 2415 Eisenhower Avenue, Alexandria, VA 22314 (jwang@nsf.gov). Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics",
year = "2020",
doi = "10.1137/17M1126618",
language = "English",
volume = "58",
pages = "2632--2661",
journal = "SIAM Journal on Numerical Analysis",
issn = "0036-1429",
number = "5",
}