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Volume 19, Issue 2-3
A Weighted Least-Squares Finite Element Method for Biot’s Consolidation Problem

Hsueh-Chen Lee & Hyesuk Lee

Int. J. Numer. Anal. Mod., 19 (2022), pp. 386-403.

Published online: 2022-04

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  • Abstract

This paper examines a weighted least-squares method for a poroelastic structure governed by Biot’s consolidation model. Quasi-static model equations are converted to a first-order system of four-field, and the least-squares functional is defined for the time discretized system. We consider two different sets of weights for the functional and show its coercivity and continuity properties, from which an a priori error estimate for the primal variables is derived. Numerical experiments are provided to illustrate the performance of the proposed method.

  • AMS Subject Headings

65N30

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-386, author = {Lee , Hsueh-Chen and Lee , Hyesuk}, title = {A Weighted Least-Squares Finite Element Method for Biot’s Consolidation Problem }, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {2-3}, pages = {386--403}, abstract = {

This paper examines a weighted least-squares method for a poroelastic structure governed by Biot’s consolidation model. Quasi-static model equations are converted to a first-order system of four-field, and the least-squares functional is defined for the time discretized system. We consider two different sets of weights for the functional and show its coercivity and continuity properties, from which an a priori error estimate for the primal variables is derived. Numerical experiments are provided to illustrate the performance of the proposed method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20487.html} }
TY - JOUR T1 - A Weighted Least-Squares Finite Element Method for Biot’s Consolidation Problem AU - Lee , Hsueh-Chen AU - Lee , Hyesuk JO - International Journal of Numerical Analysis and Modeling VL - 2-3 SP - 386 EP - 403 PY - 2022 DA - 2022/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20487.html KW - Weighted least-squares finite element method, Biot’s consolidation model. AB -

This paper examines a weighted least-squares method for a poroelastic structure governed by Biot’s consolidation model. Quasi-static model equations are converted to a first-order system of four-field, and the least-squares functional is defined for the time discretized system. We consider two different sets of weights for the functional and show its coercivity and continuity properties, from which an a priori error estimate for the primal variables is derived. Numerical experiments are provided to illustrate the performance of the proposed method.

Hsueh-Chen Lee & Hyesuk Lee. (2022). A Weighted Least-Squares Finite Element Method for Biot’s Consolidation Problem . International Journal of Numerical Analysis and Modeling. 19 (2-3). 386-403. doi:
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