Finite dimensional approximation of nonlinear problems. I: Branches of nonsingular solutions

From MaRDI portal
Publication:1166233

DOI10.1007/BF01395985zbMath0488.65021OpenAlexW2884403958WikidataQ57386831 ScholiaQ57386831MaRDI QIDQ1166233

Pierre-Arnaud Raviart, Jacques Rappaz, Franco Brezzi

Publication date: 1980

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132686



Related Items

Finite element approximation of a periodic Ginzburg-Landau model for type-II superconductors, Fully discrete finite element approximations of the forced Fisher equation, A unified framework for two-grid methods for a class of nonlinear problems, The approximation of generalized turning points by projection methods with superconvergence to the critical parameter, Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition, Resolution and implementation of the nonstationary vorticity velocity pressure formulation of the Navier-Stokes equations, Multiplicity of nodal solutions in classical non-degenerate logistic equations, Mortar spectral element discretization of the Stokes problem in domain with corners, Analysis of a full discretization scheme for \(2D\) radiative-conductive heat transfer systems, Convergence of the Kleiser Schumann method for the Navier-Stokes equations, The least-squares pseudo-spectral method for Navier-Stokes equations, Semidiscrete approximations of optimal Robin boundary control problems constrained by semilinear parabolic PDE, A staggered discontinuous Galerkin method for quasi-linear second order elliptic problems of nonmonotone type, Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points, Analysis, approximation, and computation of a coupled solid/fluid temperature control problem, Spectral discretization of the time-dependent Navier-Stokes problem with mixed boundary conditions, Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants, Error analysis of finite element approximations of the optimal control problem for stochastic Stokes equations with additive white noise, Adaptive methods for semi-linear elliptic equations with critical exponents and interior singularities, Spectral discretization of Darcy's equations with pressure dependent porosity, On the application of reduced basis methods to bifurcation problems in incompressible fluid dynamics, Mathematical and numerical aspects of a phase-field approach to critical nuclei morphology in solids, A priori error analysis of the implicit Euler, spectral discretization of a nonlinear equation for a flow in a partially saturated porous media, An incompressible fluid in a weakly deformable shell. I: Analysis of the model, A posteriori analysis of iterative algorithms for a nonlinear problem, Optimal error estimates for the pseudostress formulation of the Navier-Stokes equations, Certified reduced basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height, Error analysis for the finite element approximation of the Darcy-Brinkman-Forchheimer model for porous media with mixed boundary conditions, Une méthode numérique pour le calcul des points de retournement. Application à un problème aux limites non-linéaire. I: Étude théorique et experimentation de la méthode, Legendre and Chebyshev spectral approximations of Burgers' equation, Finite element simulations of window Josephson junctions, Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs, Approximation of Hopf bifurcation, Error analysis of a subgrid eddy viscosity multi-scale discretization of the Navier-Stokes equations, Certified reduced basis approximation for the coupling of viscous and inviscid parametrized flow models, Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs, Choice of the penalty parameter for the finite element discretization of Navier-Stokes equations., Finite element methods for semilinear elliptic problems with smooth interfaces, Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds., Numerical analysis for eversion in elastic spherical caps equilibrium, A stabilized multi-level method for non-singular finite volume solutions of the stationary 3D Navier-Stokes equations, The numerical computation of compressed states of nonlinearly elastic anisotropic plates, An optimization based domain decomposition method for partial differential equations, Numerical Liapunov-Schmidt spectral method for \(k\)-determined problems, Nonlinear finite elements: sub- and supersolutions for the heterogeneous logistic equation, On the least-squares method, Spiraling bifurcation diagrams in superlinear indefinite problems, Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition. II, A posteriori error estimators for the Stokes equations. II: Non- conforming discretizations, Spectral discretization of the time-dependent Navier-Stokes problem coupled with the heat equation, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics., Algebraic pressure segregation methods for the incompressible Navier-Stokes equations, On the impossibility of arbitrary deformations in nonlinear elasticity, A stabilized finite element method based on local polynomial pressure projection for the stationary Navier-Stokes equations, An LP empirical quadrature procedure for reduced basis treatment of parametrized nonlinear PDEs, A priori error estimates of finite element solutions of parametrized strongly nonlinear boundary value problems, A \(C^0\) interior penalty method for a von Kármán plate, Topological instabilities in families of semilinear parabolic problems subject to nonlinear perturbations, Spectral projective Newton-methods for quasilinear elliptic boundary value problems, Numerical analysis of the Navier-Stokes/Darcy coupling, Numerical solutions for nonlinear elliptic problems based on first-order system, Analysis of least squares pseudo-spectral method for the interface problem of the Navier-Stokes equations, Convergence of multi-level algorithms for a class of nonlinear problems, Vorticity-velocity-pressure formulation for Navier-Stokes equations, Discretization of the Navier-Stokes equations with slip boundary condition. II, Optimal order error estimates for finite element approximations of a bifurcation function, Optimal control problems for the two dimensional Rayleigh-Bénard type convection by a gradient method, Interior penalty method for the indefinite time-harmonic Maxwell equations, Hessian discretisation method for fourth-order semi-linear elliptic equations: applications to the von Kármán and Navier-Stokes models, Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method, Finite element approximation of some indefinite elliptic problems, Finite dimensional approximation of nonlinear problems. II: Limit points, Finite dimensional approximation of nonlinear problems. III: Simple bifurcation points, A domain decomposition algorithm for optimal control problems governed by elliptic PDEs with random inputs, Numerical analysis of a finite element projection-based VMS turbulence model with wall laws, Finite element approximation to nonlinear coupled thermal problem, New numerical studies for Darcy's problem coupled with the heat equation, Discontinuous Galerkin reduced basis empirical quadrature procedure for model reduction of parametrized nonlinear conservation laws, Finite element approximations of an optimal control problem associated with the scalar Ginzburg-Landau equation, Nodal solutions of weighted indefinite problems, Assessment of self-adapting local projection-based solvers for laminar and turbulent industrial flows, Solution manifolds and submanifolds of parametrized equations and their discretization errors, Reduced basis method for multi-parameter-dependent steady Navier-Stokes equations: applications to natural convection in a cavity, Finite element methods for semilinear elliptic and parabolic interface problems, A mixed stream-function and vorticity formulation for axisymmetric Navier-Stokes equations, Regularization and computation of a bifurcation problem with corank 2, A unified analysis of mixed and stabilized finite element solutions of Navier-Stokes equations, Computational error estimates and adaptive processes for some nonlinear structural problems, The effect of varying coefficients on the dynamics of a class of superlinear indefinite reaction-diffusion equations, Continuation of Galerkin approximations for reaction-diffusion problems, Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes, Finite dimensional approximation of bifurcation problems in presence of symmetries, Numerical continuation methods: a perspective, Accuracy of least-squares methods for the Navier--Stokes equations, Analysis of the \(L^2\) least-squares finite element method for the velocity-vorticity-pressure Stokes equations with velocity boundary conditions., Finite element approximations of parametrized strongly nonlinear boundary value problems., On a numerical Lyapunov-Schmidt method for operator equations, Analysis of piecewise linear approximations to the generalized Stokes problem in the velocity-stress-pressure formulation, Spectral approximation of the periodic nonperiodic Navier-Stokes equations, Novel stability patterns for the large necking of plates in tension: A numerical study, Spectral discretization of the Navier-Stokes problem with mixed boundary conditions, FREE CONVECTION WITH RADIATIVE THERMAL TRANSFER OF GREY BODIES: ANALYSIS AND APPROXIMATION BY FINITE ELEMENT METHODS, FREE CONVECTION WITH RADIATIVE THERMAL TRANSFER OF GREY BODIES: ANALYSIS AND APPROXIMATION BY FINITE ELEMENT METHODS, Spectral Galerkin approximation of Couette-Taylor flow, Semidiscrete Finite Element Methods for Linear and Semilinear Parabolic Problems with Smooth Interfaces: Some New Optimal Error Estimates, Reduced Finite Element Discretizations of the Stokes and Navier-Stokes Equations, CONVECTIVE AND RADIATIVE THERMAL TRANSFER WITH MULTIPLE REFLECTIONS: ANALYSIS AND APPROXIMATION BY A FINITE ELEMENT METHOD, Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains, ON THE GENERALIZED VON KÁRMÁN EQUATIONS AND THEIR APPROXIMATION, Numerical resolution of optimal control problem for the in-stationary Navier-Stokes equations, Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls, Analysis and finite element approximation of an optimal control problem for the Oseen viscoelastic fluid flow, A multi-level stabilized finite element method for the stationary Navier-Stokes equations, Numerical calculations of two-cell and single-cell Taylor flows, On the theory and error estimation of the reduced basis method for multi-parameter problems, An optimization based domain decomposition method for PDEs with random inputs, A priori and a posteriori error estimations for the dual mixed finite element method of the Navier‐Stokes problem, Analysis of backward Euler/spectral discretization for an evolutionary mass and heat transfer in porous medium, Mortar finite element discretization of the time dependent nonlinear Darcy's equations, Spectral discretization of an unsteady flow through a porous solid, Approximation of the bifurcation function for elliptic boundary value problems, Topology optimization for steady-state anisothermal flow targeting solids with piecewise constant thermal diffusivity, Dimension reduction in stochastic modeling of coupled problems, Justification and solvability of dynamical contact problems for generalized Marguerre–von Kármán shallow shells, Optimal convergence rates for Galerkin approximation of operator Riccati equations, An algorithm for solving the Navier-Stokes problem with mixed boundary conditions, On a certified VMS-Smagorinsky reduced basis model with LPS pressure stabilisation, Localized Model Reduction for Nonlinear Elliptic Partial Differential Equations: Localized Training, Partition of Unity, and Adaptive Enrichment, Unified a priori analysis of four second-order FEM for fourth-order quadratic semilinear problems, On a Certified Smagorinsky Reduced Basis Turbulence Model, An artificial neural network approach to bifurcating phenomena in computational fluid dynamics, Global structure of the set of 1-node solutions in a class of degenerate diffusive logistic equations, Reduced basis modelling of turbulence with well-developed inertial range, Numerical analysis of a Picard multilevel stabilization of mixed finite volume method for the 2D/3D incompressible flow with large data, Couplage des équations de Navier-Stokes et de la chaleur : le modèle et son approximation par éléments finis, Optimal \(L^2\), \(H^1\) and \(L^{\infty}\) analysis of finite volume methods for the stationary Navier-Stokes equations with large data, SUPERCONVERGENCE OF FEMS AND NUMERICAL CONTINUATION FOR PARAMETER-DEPENDENT PROBLEMS WITH FOLDS, Multilevel higher-order quasi-Monte Carlo Bayesian estimation, NUMERICAL ANALYSIS OF THE PSI SOLUTION OF ADVECTION–DIFFUSION PROBLEMS THROUGH A PETROV–GALERKIN FORMULATION, Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow, Computation of Morse decompositions for semilinear elliptic PDEs, Finite element analysis of the buckling and mode jumping of a rectangular plate, Spectral element discretization of the vorticity,velocity and pressure formulation of the Navier-Stokes problem, Problems of mhd stability in thermonuclear fusion plasmas, Numerical Analysis of an Optimal Control Problem Governed by the Stationary Navier-Stokes Equations with Global Velocity-Constrained, Primal mixed finite-element approximation of elliptic equations with gradient nonlinearities, Newton's method for the Navier-Stokes equations with finite element initial guess of Stokes equations, A space-time hp-interpolation-based certified reduced basis method for Burgers' equation, An optimization-based domain decomposition method for a nonlinear problem, Error analysis of a weighted least-squares finite element method for 2-D incompressible flows in velocity-stress-pressure formulation, Least-Squares Methods for Navier-Stokes Boundary Control Problems, Sparse Grid Collocation Method for an Optimal Control Problem Involving a Stochastic Partial Differential Equation with Random Inputs, Approximation numérique de certaines équations paraboliques non linéaires, An optimization-based domain decomposition method for the Boussinesq equations, Finite element analysis for parametrized nonlinear equations around turning points, A Posteriori Least-Squares Finite Element Error Analysis for the Navier–Stokes Equations, An efficient discretization of the Navier-Stokes equations in an axisymmetric domain. I: The discrete problem and its numerical analysis, Spectral discretization of the vorticity, velocity and pressure formulation of the Navier-Stokes equations, Edge finite elements for the approximation of Maxwell resolvent operator, On the existence and numerical computation of classical and non-classical solutions for a family of elliptic boundary value problems, Analysis of a quasicontinuum method in one dimension, An Augmented Mixed Finite Element Method for the Navier--Stokes Equations with Variable Viscosity, Finite element discretization of Darcy's equations with pressure dependent porosity, Residual-based a posteriori error estimates for a conforming mixed finite element discretization of the Monge-Amp\`ere equation, Convergence of a fluid-structure interaction problem decoupled by a Neumann control over a single time step, EXISTENCE AND CONVERGENCE RESULTS FOR THE GALERKIN APPROXIMATION OF AN ELECTRONIC DENSITY FUNCTIONAL, Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes, Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models, Unnamed Item, On First-order Formulations of the Least-squares Finite Element Method for Incompressible Flows, AUTOMATIC INSERTION OF A TURBULENCE MODEL IN THE FINITE ELEMENT DISCRETIZATION OF THE NAVIER–STOKES EQUATIONS, A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions, Analysis of cell size effects in atomistic crack propagation, Approximation of Burgers' equation by pseudo-spectral methods, Approximation of solution branches of nonlinear equations, Reduced basis approaches for parametrized bifurcation problems held by non-linear von Kármán equations, Numerical Continuation at Double Bifurcation Points of a Reaction–Diffusion Problem, Space-time registration-based model reduction of parameterized one-dimensional hyperbolic PDEs, Finite Element Discretization of the Stokes and Navier--Stokes Equations with Boundary Conditions on the Pressure, Two-grid methods for semilinear interface problems, Spectral discretization of the Navier–Stokes equations coupled with the heat equation, Global bifurcation diagrams of positive solutions for a class of 1D superlinear indefinite problems*, Intricate dynamics caused by facilitation in competitive environments within polluted habitat patches



Cites Work