TY - JOUR
T1 - A Simple Finite Element Method for Non-Divergence form Elliptic Equations
AU - L. Mu & X. Ye
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 306
EP - 311
PY - 2016
DA - 2016/05
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/422.html
KW - Finite element methods, non-divergence form elliptic equations, polyhedral meshes.
AB - <p style="text-align: justify;">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. Also general meshes with polytopal element and hanging node can be used 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.</p>