A simple finite element method for nondivergence form elliptic equation
Here, we develop a simple finite element method for solving second order elliptic equations in nondivergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.
 Authors:

^{[1]};
^{[2]}
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
 Univ. of Arkansas, Little Rock, AR (United States). Dept. of Mathematics
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 International Journal of Numerical Analysis and Modeling
 Additional Journal Information:
 Journal Volume: 14; Journal Issue: 2; Journal ID: ISSN 17055105
 Publisher:
 Institute for Scientific Computing and Information
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; finite element methods; nondivergence form elliptic equations; polyhedral meshes
 OSTI Identifier:
 1346680
Mu, Lin, and Ye, Xiu. A simple finite element method for nondivergence form elliptic equation. United States: N. p.,
Web.
Mu, Lin, & Ye, Xiu. A simple finite element method for nondivergence form elliptic equation. United States.
Mu, Lin, and Ye, Xiu. 2017.
"A simple finite element method for nondivergence form elliptic equation". United States.
doi:. https://www.osti.gov/servlets/purl/1346680.
@article{osti_1346680,
title = {A simple finite element method for nondivergence form elliptic equation},
author = {Mu, Lin and Ye, Xiu},
abstractNote = {Here, we develop a simple finite element method for solving second order elliptic equations in nondivergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.},
doi = {},
journal = {International Journal of Numerical Analysis and Modeling},
number = 2,
volume = 14,
place = {United States},
year = {2017},
month = {3}
}