Analysis of the \(L^2\) least-squares finite element method for the velocity-vorticity-pressure Stokes equations with velocity boundary conditions.

DOI10.1016/S0096-3003(01)00086-8zbMath1126.76316OpenAlexW2028587964MaRDI QIDQ1855727

Suh-Yuh Yang, Ching-Lung Chang

Publication date: 28 January 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(01)00086-8

zbMATH Keywords

ConvergenceStabilityA priori error estimatesLeast-squares finite element methodsCondition numbersVelocity-vorticity-pressure Stokes equations

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items

Performance of nonconforming spectral element method for Stokes problems, Quasi-least-squares finite element method for steady flow and heat transfer with system rotation, Analysis of a splitting method for incompressible inviscid rotational flow problems, First order least squares method with weakly imposed boundary condition for convection dominated diffusion problems, Analysis of the \(L^{2}\) least-squares finite element method for a velocity-vorticity problem arising in incompressible inviscid rotational flows, Weighted least-squares finite element methods for the linearized Navier–Stokes equations, Least‐squares formulations for Stokes equations with non‐standard boundary conditions—A unified approach, A weighted least-squares finite element method for Phan-Thien-Tanner viscoelastic fluid, On efficient least-squares finite element methods for convection-dominated problems, Improving convergence by optimizing the condition number of the stiffness matrices arising from least-squares finite element methods, Adaptive weights for mass conservation in a least-squares finite element method, A nonlinear weighted least-squares finite element method for the Oldroyd-B viscoelastic flow, Analysis of \(H^{-1},L^{2},L^{2}\) first-order system least squares for the incompressible Oseen type equations, A least-squares finite element method for the Navier--Stokes equations, On mass conservation in least-squares methods, On the velocity-vorticity-pressure least-squares finite element method for the stationary incompressible Oseen problem, Non-conforming least-squares spectral element method for Stokes equations on non-smooth domains, On Two Iterative Least-Squares Finite Element Schemes for the Incompressible Navier–Stokes Problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Least-squares finite element method for fluid dynamics
• An error analysis of least-squares finite element method of velocity- pressure-vorticity formulation for Stokes problem
• A mixed finite element method for the Stokes problem: an acceleration-pressure formulation
• Least-squares finite elements for the Stokes problem
• On finite element methods of the least squares type
• Finite dimensional approximation of nonlinear problems. I: Branches of nonsingular solutions
• On the convergence and stability of the standard least squares finite element method for first-order elliptic systems
• A unified analysis of a weighted least squares method for first-order systems
• Accuracy of least-squares methods for the Navier--Stokes equations
• Least-squares methods for the velocity-pressure-stress formulation of the Stokes equations.
• First-order system least squares for velocity-vorticity-pressure form of the Stokes equations, with application to linear elasticity
• Least-squares methods for Stokes equations based on a discrete minus one inner product
• A least-squares finite element method for incompressible flow in stress-velocity-pressure version
• Adaptive refinement for least-squares finite elements with element-by-element conjugate gradient solution
• A Comparative Study of Finite Element and Finite Difference Methods for Cauchy-Riemann Type Equations
• Finite Element Methods for Navier-Stokes Equations
• Least Squares Methods for Elliptic Systems
• Finite element approximation of vector fields given by curl and divergence
• Mixed and Hybrid Finite Element Methods
• Finite Element Approximation for Grad-Div Type Systems in the Plane
• A least-squares finite element method for incompressible Navier-Stokes problems
• Error analysis of a weighted least-squares finite element method for 2-D incompressible flows in velocity-stress-pressure formulation
• A two-stage least-squares finite element method for the stress-pressure-displacement elasticity equations
• An Error Estimate of the Least Squares Finite Element Method for the Stokes Problem in Three Dimensions
• Least-Squares Mixed Finite Elements for Second-Order Elliptic Problems
• Analysis of Least Squares Finite Element Methods for the Stokes Equations
• First-Order System Least Squares for Second-Order Partial Differential Equations: Part I
• First-Order System Least Squares for Second-Order Partial Differential Equations: Part II
• Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation
• First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity
• Analysis of Least-Squares Finite Element Methods for the Navier--Stokes Equations
• Analysis of Velocity-Flux First-Order System Least-Squares Principles for the Navier--Stokes Equations: Part I
• Rayleigh‐Ritz‐Galerkin methods for dirichlet's problem using subspaces without boundary conditions
• Least Squares Methods for 2mth Order Elliptic Boundary-Value Problems
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
• A Subdomain–Galerkin/Least Squares Method for First-Order Elliptic Systems in the Plane