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Volume 8, Issue 2
Optimal Error Estimates of the Local Discontinuous Galerkin Method for Willmore Flow of Graphs on Cartesian Meshes

L. Ji & Y. Xu

Int. J. Numer. Anal. Mod., 8 (2011), pp. 252-283.

Published online: 2011-08

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  • Abstract

In this paper, we analyze a local discontinuous Galerkin method for the willmore flow of graphs. We derive the optimal error estimates for this nonlinear equation in one-dimension and in multi-dimensions for Cartesian meshes using completely discontinuous piecewise polynomial space with degree $k \leq 1$.

  • Keywords

local discontinuous Galerkin method, Willmore flow of graphs, stability, error estimates.

  • AMS Subject Headings

65M60, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-252, author = {L. Ji and Y. Xu}, title = {Optimal Error Estimates of the Local Discontinuous Galerkin Method for Willmore Flow of Graphs on Cartesian Meshes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {2}, pages = {252--283}, abstract = {

In this paper, we analyze a local discontinuous Galerkin method for the willmore flow of graphs. We derive the optimal error estimates for this nonlinear equation in one-dimension and in multi-dimensions for Cartesian meshes using completely discontinuous piecewise polynomial space with degree $k \leq 1$.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/685.html} }
TY - JOUR T1 - Optimal Error Estimates of the Local Discontinuous Galerkin Method for Willmore Flow of Graphs on Cartesian Meshes AU - L. Ji & Y. Xu JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 252 EP - 283 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/685.html KW - local discontinuous Galerkin method, Willmore flow of graphs, stability, error estimates. AB -

In this paper, we analyze a local discontinuous Galerkin method for the willmore flow of graphs. We derive the optimal error estimates for this nonlinear equation in one-dimension and in multi-dimensions for Cartesian meshes using completely discontinuous piecewise polynomial space with degree $k \leq 1$.

L. Ji and Y. Xu. (2011). Optimal Error Estimates of the Local Discontinuous Galerkin Method for Willmore Flow of Graphs on Cartesian Meshes. International Journal of Numerical Analysis and Modeling. 8 (2). 252-283. doi:
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