Optimal least-squares finite element method for elliptic problems

DOI10.1016/0045-7825(93)90108-AzbMath0809.65104MaRDI QIDQ1802839

Louis A. Povinelli, Bo-Nan Jiang

Publication date: 29 June 1993

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

zbMATH Keywords

first-order systemconvergencenumerical experimentserror analysiselliptic problemssecond-order equationmixed Galerkin methodoptimal least squares finite element method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (20)

A discontinuous least-squares finite-element method for second-order elliptic equations ⋮ The least-squares finite element method in elasticity. Part II: Bending of thin plates ⋮ Unnamed Item ⋮ Quasi-least-squares finite element method for steady flow and heat transfer with system rotation ⋮ A div-curl-grad formulation for compressible buoyant flows solved by the least-squares finite element method ⋮ Asymptotic Exactness of the Least-Squares Finite Element Residual ⋮ A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations ⋮ A least-squares approach based on a discrete minus one inner product for first order systems ⋮ A least-squares virtual element method for second-order elliptic problems ⋮ Parallel least-squares finite element method for time-dependent convection-diffusion system ⋮ Some least-squares Galerkin procedures for first-order time-dependent convection-diffusion system ⋮ Least-squares solutions as solutions of a perturbation form of the Galerkin methods: interior pointwise error estimates and pollution effect ⋮ A least-squares method for optimal control problems for a second-order elliptic system in two dimensions ⋮ Least-Squares Methods for Navier-Stokes Boundary Control Problems ⋮ Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems ⋮ A Sequential Least Squares Method for Poisson Equation Using a Patch Reconstructed Space ⋮ A least-squares/penalty method for distributed optimal control problems for Stokes equations ⋮ Analysis of a least-squares finite element method for the thin plate problem ⋮ An a posteriori error estimator for the weak Galerkin least-squares finite-element method ⋮ Three-dimensional simulations of Marangoni-Benard convection in small containers by the least-squares finite element method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite element approximation of the Navier-Stokes equations
• Adaptive refinement for least-squares finite elements with element-by-element conjugate gradient solution
• The Generalized Finite Element Method—State of the Art and Future Directions
• A Comparative Study of Finite Element and Finite Difference Methods for Cauchy-Riemann Type Equations
• Least Squares Methods for Elliptic Systems
• Finite elements formulated by the weighted discrete least squares method

This page was built for publication: Optimal least-squares finite element method for elliptic problems