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Volume 10, Issue 4
A Comment on Least-Squares Finite Element Methods with Minimum Regularity Assumptions

J. Ku

Int. J. Numer. Anal. Mod., 10 (2013), pp. 899-903.

Published online: 2013-10

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  • Abstract

Least-squares(LS) finite element methods are applied successfully to a wide range of problems arising from science and engineering. However, there are reservations to use LS methods for problems with low regularity solutions. In this paper, we consider LS methods for second-order elliptic problems using the minimum regularity assumption, i.e. the solution only belongs to $H^1$ space. We provide a theoretical analysis showing that LS methods are competitive alternatives to mixed and standard Galerkin methods by establishing that LS solutions are bounded by the mixed and standard Galerkin solutions.

  • Keywords

least-squares, finite element methods, Galerkin methods.

  • AMS Subject Headings

65N30, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-10-899, author = {J. Ku}, title = {A Comment on Least-Squares Finite Element Methods with Minimum Regularity Assumptions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {4}, pages = {899--903}, abstract = {

Least-squares(LS) finite element methods are applied successfully to a wide range of problems arising from science and engineering. However, there are reservations to use LS methods for problems with low regularity solutions. In this paper, we consider LS methods for second-order elliptic problems using the minimum regularity assumption, i.e. the solution only belongs to $H^1$ space. We provide a theoretical analysis showing that LS methods are competitive alternatives to mixed and standard Galerkin methods by establishing that LS solutions are bounded by the mixed and standard Galerkin solutions.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/602.html} }
TY - JOUR T1 - A Comment on Least-Squares Finite Element Methods with Minimum Regularity Assumptions AU - J. Ku JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 899 EP - 903 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/602.html KW - least-squares, finite element methods, Galerkin methods. AB -

Least-squares(LS) finite element methods are applied successfully to a wide range of problems arising from science and engineering. However, there are reservations to use LS methods for problems with low regularity solutions. In this paper, we consider LS methods for second-order elliptic problems using the minimum regularity assumption, i.e. the solution only belongs to $H^1$ space. We provide a theoretical analysis showing that LS methods are competitive alternatives to mixed and standard Galerkin methods by establishing that LS solutions are bounded by the mixed and standard Galerkin solutions.

J. Ku. (2013). A Comment on Least-Squares Finite Element Methods with Minimum Regularity Assumptions. International Journal of Numerical Analysis and Modeling. 10 (4). 899-903. doi:
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