Error Analysis of an Immersed Finite Element Method for Euler-Bernoulli Beam Interface Problems

Volume 14, Issue 6

Min Lin, Tao Lin & Huili Zhang

DOI:

Int. J. Numer. Anal. Mod., 14 (2017), pp. 822-841

Published online: 2017-10

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Abstract

This article presents an error analysis of a Hermite cubic immersed finite element (IFE) method for solving interface problems of the differential equation modeling a Euler-Bernoulli beam made up of multiple materials together with suitable jump conditions at material interfaces. The analysis consists of three essential groups. The first group is about IFE functions including bounds for the IFE shape functions and inverse inequalities. The second group is about error bounds for IFE interpolation derived with a multi-point Taylor expansion technique. The last group, and perhaps the most important group, is for proving the optimal convergence of the IFE solution generated by the usual Galerkin scheme based on the Hermite cubic IFE space considered in this article.

Keywords

Error estimation interface problem interface independent mesh Euler-Bernoulli beam Hermite cubic finite element multi-point Taylor expansion optimal convergence

AMS Subject Headings

65N15 65N30 65N50 35R05.

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@Article{IJNAM-14-822, author = {Min Lin, Tao Lin and Huili Zhang}, title = {Error Analysis of an Immersed Finite Element Method for Euler-Bernoulli Beam Interface Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {6}, pages = {822--841}, abstract = {This article presents an error analysis of a Hermite cubic immersed finite element (IFE) method for solving interface problems of the differential equation modeling a Euler-Bernoulli beam made up of multiple materials together with suitable jump conditions at material interfaces. The analysis consists of three essential groups. The first group is about IFE functions including bounds for the IFE shape functions and inverse inequalities. The second group is about error bounds for IFE interpolation derived with a multi-point Taylor expansion technique. The last group, and perhaps the most important group, is for proving the optimal convergence of the IFE solution generated by the usual Galerkin scheme based on the Hermite cubic IFE space considered in this article.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10482.html} }

TY - JOUR T1 - Error Analysis of an Immersed Finite Element Method for Euler-Bernoulli Beam Interface Problems AU - Min Lin, Tao Lin & Huili Zhang JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 822 EP - 841 PY - 2017 DA - 2017/10 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10482.html KW - Error estimation KW - interface problem KW - interface independent mesh KW - Euler-Bernoulli beam KW - Hermite cubic finite element KW - multi-point Taylor expansion KW - optimal convergence AB - This article presents an error analysis of a Hermite cubic immersed finite element (IFE) method for solving interface problems of the differential equation modeling a Euler-Bernoulli beam made up of multiple materials together with suitable jump conditions at material interfaces. The analysis consists of three essential groups. The first group is about IFE functions including bounds for the IFE shape functions and inverse inequalities. The second group is about error bounds for IFE interpolation derived with a multi-point Taylor expansion technique. The last group, and perhaps the most important group, is for proving the optimal convergence of the IFE solution generated by the usual Galerkin scheme based on the Hermite cubic IFE space considered in this article.

Min Lin, Tao Lin & Huili Zhang. (1970). Error Analysis of an Immersed Finite Element Method for Euler-Bernoulli Beam Interface Problems. International Journal of Numerical Analysis and Modeling. 14 (6). 822-841. doi:

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