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Title: A simple finite element method for non-divergence form elliptic equation

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence 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]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
  2. Univ. of Arkansas, Little Rock, AR (United States). Dept. of Mathematics
Publication Date:
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
International Journal of Numerical Analysis and Modeling
Additional Journal Information:
Journal Volume: 14; Journal Issue: 2; Journal ID: ISSN 1705-5105
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) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; finite element methods; non-divergence form elliptic equations; polyhedral meshes
OSTI Identifier:
1346680