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Least-squares mixed finite elements for second-order elliptic problems
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In this paper, a theoretical analysis of a least-squares mixed finite element method for second-order elliptic problems in two-and three-dimensional domains is presented, and it is proved that the method is not subj...Abstract:
A theoretical analysis of a least-squares mixed finite element method for second-order elliptic problems in two- and three-dimensional domains is presented. It is proved that the method is not subj...read more
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Least-Squares Finite Element Methods
TL;DR: This paper focuses on theoretical and practical aspects of least-square finite element methods and includes discussions of what issues enter into their construction, analysis, and performance.
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First-order system least squares for second-order partial differential equations: part I
TL;DR: The least-squares approach developed here applies directly to convection--diffusion--reaction equations in a unified way and also admits a fast multigrid solver, historically a missing ingredient in least-Squares methodology.
Journal ArticleDOI
Finite Element Methods of Least-Squares Type
TL;DR: The use of least-squares principles leads to symmetric and positive definite algebraic problems and allows us to circumvent stability conditions such as the inf-sup condition arising in mixed methods for the Stokes and Navier--Stokes equations.
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Quadrilateral H (div) Finite Elements
TL;DR: This work considers the approximation properties of quadrilateral finite element spaces of vector fields defined by the Piola transform, and derives new estimates for approximation byquadrilateral Raviart--Thomas elements (requiring less regularity) and proposes a new quadrilaterally finite element space which provides optimal order approximation in H(div).
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A least-squares approach based on a discrete minus one inner product for first order systems
TL;DR: A least-squares approximation to a first order system which involves a discrete inner product which is related to the inner product in H -1 (Ω) (the Sobolev space of order minus one on Ω) results in a method of approximation which is optimal with respect to the required regularity.