A comment on least-squares finite element methods with minimum regularity assumptions (Q2865650)
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scientific article; zbMATH DE number 6235040
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A comment on least-squares finite element methods with minimum regularity assumptions |
scientific article; zbMATH DE number 6235040 |
Statements
2 December 2013
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least-squares
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finite element methods
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Galerkin methods
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second-order elliptic problem
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minimum regularity assumption
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A comment on least-squares finite element methods with minimum regularity assumptions (English)
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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, LS methods are considered for second-order elliptic problems using the minimum regularity assumption, i.e., the solution only belongs to an \(H^1\) space. A theoretical analysis is provided 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.
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