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Volume 14, Issue 4-5
A Simple Finite Element Method of the Cauchy Problem for Poisson Equation

Xiaozhe Hu, Lin Mu & Xiu Ye

Int. J. Numer. Anal. Mod., 14 (2017), pp. 591-603.

Published online: 2017-08

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  • Abstract

In this paper, we introduce a simple method for the Cauchy problem. This new finite element method is based on least squares methodology with discontinuous approximations which can be implemented and analyzed easily. This discontinuous Galerkin finite element method is flexible to work with general unstructured meshes. Error estimates of the finite element solution are derived. The numerical examples are presented to demonstrate the robustness and flexibility of the proposed method.

  • Keywords

Finite element methods, Cauchy problem, polyhedral meshes.

  • AMS Subject Headings

Primary 65N15, 65N30, 76D07, Secondary 35B45, 35J50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-591, author = {Xiaozhe Hu, Lin Mu and Xiu Ye}, title = {A Simple Finite Element Method of the Cauchy Problem for Poisson Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {4-5}, pages = {591--603}, abstract = {

In this paper, we introduce a simple method for the Cauchy problem. This new finite element method is based on least squares methodology with discontinuous approximations which can be implemented and analyzed easily. This discontinuous Galerkin finite element method is flexible to work with general unstructured meshes. Error estimates of the finite element solution are derived. The numerical examples are presented to demonstrate the robustness and flexibility of the proposed method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10051.html} }
TY - JOUR T1 - A Simple Finite Element Method of the Cauchy Problem for Poisson Equation AU - Xiaozhe Hu, Lin Mu & Xiu Ye JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 591 EP - 603 PY - 2017 DA - 2017/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10051.html KW - Finite element methods, Cauchy problem, polyhedral meshes. AB -

In this paper, we introduce a simple method for the Cauchy problem. This new finite element method is based on least squares methodology with discontinuous approximations which can be implemented and analyzed easily. This discontinuous Galerkin finite element method is flexible to work with general unstructured meshes. Error estimates of the finite element solution are derived. The numerical examples are presented to demonstrate the robustness and flexibility of the proposed method.

Xiaozhe Hu, Lin Mu and Xiu Ye. (2017). A Simple Finite Element Method of the Cauchy Problem for Poisson Equation. International Journal of Numerical Analysis and Modeling. 14 (4-5). 591-603. doi:
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