Finite Element Methods of Least-Squares Type
From MaRDI portal
Publication:4229429
DOI10.1137/S0036144597321156zbMath0914.65108MaRDI QIDQ4229429
Max D. Gunzburger, Pavel B. Bochev
Publication date: 22 February 1999
Published in: SIAM Review (Search for Journal in Brave)
Navier-Stokes equationselliptic equationssurvey papercompressible flowsinviscidelectromagnetic problemsleast-squares finite element methodsconvection-diffusion elliptic problems
Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with optics and electromagnetic theory (35Q60) Navier-Stokes equations for incompressible viscous fluids (76D05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Finite element methods applied to problems in fluid mechanics (76M10)
Related Items
Error estimates for least squares finite element methods, Error and stability estimates of a least-squares variational kernel-based method for second order elliptic PDEs, Windowed least-squares model reduction for dynamical systems, Accelerated reactive transport simulations in heterogeneous porous media using Reaktoro and Firedrake, FOSLL* for Nonlinear Partial Differential Equations, A collocation penalty least-squares finite element formulation for incompressible flows, The least-squares pseudo-spectral method for Navier-Stokes equations, Performance of nonconforming spectral element method for Stokes problems, Weighted extended B-splines for one-dimensional electromagnetic problems, Least-squares finite element formulations for viscous incompressible and compressible fluid flows, Analysis of a splitting method for incompressible inviscid rotational flow problems, A conservation-prioritized approach simultaneously enhancing mass and momentum conservation of least-squares method for Stokes/Navier-Stokes problems, Least squares finite element method with high continuity NURBS basis for incompressible Navier-Stokes equations, Stabilization of low-order mixed finite elements for the plane elasticity equations, Least-squares finite element method for shallow-water equations with source terms, 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, Space-time coupled spectral/\(hp\) least-squares finite element formulation for the incompressible Navier-Stokes equations, An adaptive mixed least-squares finite element method for viscoelastic fluids of Oldroyd type, Multiscale stabilization for convection-diffusion equations with heterogeneous velocity and diffusion coefficients, Left ventricular flow analysis: recent advances in numerical methods and applications in cardiac ultrasound, The adjoint Petrov-Galerkin method for non-linear model reduction, Multiscale stabilization for convection-dominated diffusion in heterogeneous media, A simple proof of coerciveness of first-order system least-squares methods for general second-order elliptic PDEs, A least-squares FEM-BEM coupling method for linear elasticity, Solution of shallow-water equations using least-squares finite-element method, Least-squares spectral element solution of incompressible Navier-Stokes equations with adaptive refinement, A Non-Conforming Least Squares Spectral Element Formulation for Oseen Equations with Applications to Navier-Stokes Equations, Least‐squares spectral element method applied to the Euler equations, A weighted adaptive least-squares finite element method for the Poisson-Boltzmann equation, Méthodes d'optimisation pour l'approche de problèmes aux limites non linéaires mixtes elliptiques hyperboliques. (Optimization methods for treating mixed elliptic-hyperbolic nonlinear boundary value problems), Spectral/\(hp\) least-squares finite element formulation for the Navier-Stokes equations., Convergence analysis for least-squares finite element approximations of second-order two-point boundary value problems, Spectral/hppenalty least-squares finite element formulation for unsteady incompressible flows, A least-squares virtual element method for second-order elliptic problems, Least-squares finite element methods for generalized Newtonian and viscoelastic flows, Analysis of a velocity-pressure-pseudostress formulation for the stationary Stokes equations, A priori and a posteriori error analyses of a velocity-pseudostress formulation for a class of quasi-Newtonian Stokes flows, A discrete least squares collocation method for two-dimensional nonlinear time-dependent partial differential equations, On efficient least-squares finite element methods for convection-dominated problems, Analysis and computation of a least-squares method for consistent mesh tying, An optimal projection method for the reduced-order modeling of incompressible flows, An alternative least-squares formulation of the Navier-Stokes equations with improved mass conservation, Adaptive least-squares finite element approximations to Stokes equations, Combined hybrid approach to finite element schemes of high performance, A nonlinear weighted least-squares finite element method for the Carreau-Yasuda non-Newtonian model, Localized forms of the LBB condition and a posteriori estimates for incompressible media problems, A least-squares method with direct minimization for the solution of the breakage-coalescence population balance equation, Direct minimization of the least-squares spectral element functional. I: Direct solver, A convergence result for a least-squares method using Schauder bases, Numerical simulations of viscoelastic fluid flows past a transverse slot using least-squares finite element methods, Least-squares spectral element method for non-linear hyperbolic differential equations, A least-squares finite element method for a nonlinear Stokes problem in glaciology, On the roles of minimization and linearization in least-squares finite element models of nonlinear boundary-value problems, Analysis of \(H^{-1},L^{2},L^{2}\) first-order system least squares for the incompressible Oseen type equations, Discrete weighted least-squares method for the Poisson and biharmonic problems on domains with smooth boundary, A least-squares finite element method for the Navier--Stokes equations, On mass conservation in least-squares methods, A least squares coupling method with finite elements and boundary elements for transmission problems, Least-squares finite-element methods for optimization and control problems for the Stokes equations, On the velocity-vorticity-pressure least-squares finite element method for the stationary incompressible Oseen problem, Application of the least-squares spectral element method using Chebyshev polynomials to solve the incompressible Navier-Stokes equations, The use of Chebyshev polynomials in the space-time least-squares spectral element method, Introduction to the web-method and its applications, A nonlinear weighted least-squares finite element method for Stokes equations, Mixed finite elements of least-squares type for elasticity, Dual-mixed finite element approximation of Stokes and nonlinear Stokes problems using trace-free velocity gradients, Higher-order Gauss-Lobatto integration for nonlinear hyperbolic equations, Analysis of a non-standard mixed finite element method with applications to superconvergence, Numerical study of natural superconvergence in least-squares finite element methods for elliptic problems, A minimum-residual mixed reduced basis method: Exact residual certification and simultaneous finite-element reduced-basis refinement, A least-squares formulation of the moving discontinuous Galerkin finite element method with interface condition enforcement, On the efficiency of combining different methods for acceleration of iterations at the solution of PDEs by the method of collocations and least residuals, Adjoint pseudospectral least-squares methods for an elliptic boundary value problem, Spectral solution of the breakage-coalescence population balance equation Picard and Newton iteration methods, Least-squares mixed finite elements for small strain elasto-viscoplasticity, A displacement smoothing induced strain gradient stabilization for the meshfree Galerkin nodal integration method, Pseudo-spectral least squares method for linear elasticity, A least-squares/penalty method for distributed optimal control problems for Stokes equations, Non-conforming least-squares spectral element method for Stokes equations on non-smooth domains, Analysis of a least-squares finite element method for the thin plate problem, Discontinuous Galerkin least-squares finite element methods for singularly perturbed reaction-diffusion problems with discontinuous coefficients and boundary singularities, A least-squares finite element method for steady flows across an unconfined square cylinder placed symmetrically in a plane channel, A computational study of stabilized, low-order \(C^{0}\) finite element approximations of Darcy equations, A least squares method for linear elasticity using a patch reconstructed space, Fictitious domain approach with \(hp\)-finite element approximation for incompressible fluid flow, On Two Iterative Least-Squares Finite Element Schemes for the Incompressible Navier–Stokes Problem, New mixed finite elements for plane elasticity and Stokes equations, A bubble-stabilized least-squares finite element method for steady MHD duct flow problems at high Hartmann numbers, Least-squares methods for elasticity and Stokes equations with weakly imposed symmetry, Weighted least-squares finite elements based on particle imaging velocimetry data, Discontinuous least-squares finite element method for the div-curl problem, Least-squares spectral elements applied to the Stokes problem, Analysis of piecewise linear approximations to the generalized Stokes problem in the velocity-stress-pressure formulation, Dual system least-squares finite element method for a hyperbolic problem, Least-squares spectral element method for three dimensional Stokes equations, ANALYSIS OF LEAST-SQUARES APPROXIMATIONS TO SECOND-ORDER ELLIPTIC PROBLEMS. I. FINITE ELEMENT METHOD, ANALYSIS OF LEAST-SQUARES APPROXIMATIONS TO SECOND-ORDER ELLIPTIC PROBLEMS. II. FINITE VOLUME METHOD, Least-squares finite element formulation for shear-deformable shells, Multidomain Legendre-Galerkin Chebyshev collocation least squares method for one-dimensional problems with two nonhomogeneous jump conditions, The least-squares finite element method in elasticity. Part II: Bending of thin plates, Least-squares method for recovering multiple medium parameters, Stability of a trilinear-trilinear approximation for the Stokes equations, VPVnet: A Velocity-Pressure-Vorticity Neural Network Method for the Stokes’ Equations under Reduced Regularity, DISCONTINUOUS/CONTINUOUS LEAST-SQUARES FINITE ELEMENT METHODS FOR ELLIPTIC PROBLEMS, A discontinuous least squares finite element method for the Helmholtz equation, Least‐squares formulations for Stokes equations with non‐standard boundary conditions—A unified approach, Least-squares virtual element method for Stokes problems on polygonal meshes, The least-squares finite element method in elasticity?Part I: Plane stress or strain with drilling degrees of freedom, A Reduced Basis Method for Coercive Equations with an Exact Solution Certificate and Spatio-Parameter Adaptivity: Energy-Norm and Output Error Bounds, A NEW MINIMIZATION PRINCIPLE FOR THE POISSON EQUATION LEADING TO A FLEXIBLE FINITE ELEMENT APPROACH, A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems, Variants of the Finite Element Method for the Parabolic Heat Equation: Comparative Numerical Study, Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems, A weighted least squares finite element method for elliptic problems with degenerate and singular coefficients, Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains, A Posteriori Least-Squares Finite Element Error Analysis for the Navier–Stokes Equations, Stabilized hybrid finite element methods based on the combination of saddle point principles of elasticity problems, Least-squares methods for linear elasticity based on a discrete minus one inner product, Nonconforming elements in least-squares mixed finite element methods, A Sequential Least Squares Method for Poisson Equation Using a Patch Reconstructed Space, On First-order Formulations of the Least-squares Finite Element Method for Incompressible Flows, A Sequential Least Squares Method for Elliptic Equations in Non-Divergence Form
