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Volume 14, Issue 2
A Simple Finite Element Method for Non-Divergence form Elliptic Equations

L. Mu & X. Ye

Int. J. Numer. Anal. Mod., 14 (2017), pp. 306-311.

Published online: 2016-05

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  • Abstract

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.

  • Keywords

Finite element methods, non-divergence form elliptic equations, polyhedral meshes.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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  • BibTex
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@Article{IJNAM-14-306, author = {L. Mu and X. Ye}, title = {A Simple Finite Element Method for Non-Divergence form Elliptic Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {14}, number = {2}, pages = {306--311}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/422.html} }
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 -

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.

L. Mu and X. Ye. (2016). A Simple Finite Element Method for Non-Divergence form Elliptic Equations. International Journal of Numerical Analysis and Modeling. 14 (2). 306-311. doi:
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