Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations

DOI10.1137/140971890zbMath1312.65005arXiv1407.4558OpenAlexW2008849850MaRDI QIDQ5253549

Rob Falgout, Shun Zhang, Zhi-qiang Cai

Publication date: 27 May 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.4558

zbMATH Keywords

least-squares methodelliptic equationsa posteriori error estimatea priori error estimateLL* method

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items (10)

A priori error analysis of high-order LL* (FOSLL*) finite element methods ⋮ FOSLL* for Nonlinear Partial Differential Equations ⋮ An \(L^2\)-finite element approximation of the solution to div/curl-systems with nonempty null space ⋮ Dual least‐squares finite element method with stabilization ⋮ A simple proof of coerciveness of first-order system least-squares methods for general second-order elliptic PDEs ⋮ A div FOSLS method suitable for quadrilateral RT and hexahedral RTN \(H(\operatorname{div})\)-elements ⋮ Least-squares methods with nonconforming finite elements for general second-order elliptic equations ⋮ How to prove optimal convergence rates for adaptive least-squares finite element methods ⋮ Adaptive First-Order System Least-Squares Finite Element Methods for Second-Order Elliptic Equations in Nondivergence Form ⋮ Weighted norm least squares finite element method for Poisson equation in a polyhedral domain

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• On Least-Squares Finite Element Methods for the Poisson Equation and Their Connection to the Dirichlet and Kelvin Principles
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