Convergence analysis of a minimax method for finding multiple solutions of semilinear elliptic equation.: I: On polyhedral domain

DOI10.1007/S10915-014-9871-8zbMath1320.65156OpenAlexW1993032482MaRDI QIDQ2355553

Xudong Yao

Publication date: 24 July 2015

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-014-9871-8

zbMATH Keywords

convergencefinite element methodmultiple solutionsminimax methodsemilinear elliptic equationpolyhedral domain

Mathematics Subject Classification ID

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) Semilinear elliptic equations (35J61)

Related Items (6)

Ljusternik-Schnirelman minimax algorithms and an application for finding multiple negative energy solutions of semilinear elliptic Dirichlet problem involving concave and convex nonlinearities. I: Algorithms and convergence ⋮ A Ljusternik-Schnirelman minimax algorithm for finding equality constrained saddle points and its application for solving eigen problems. I. Algorithm and global convergence ⋮ Two classes of Ljusternik-Schnirelman minimax algorithms and an application for finding multiple negative energy solutions of a class of \(p\)-Laplacian equations ⋮ A minimax algorithm based on Newton's method and an application for finding multiple solutions of p‐area problems ⋮ A local min-orthogonal based numerical method for computing multiple coexisting solutions to cooperative \(p\)-Laplacian systems ⋮ Adaptive Local Minimax Galerkin Methods for Variational Problems

Cites Work

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• Finding multiple solutions to elliptic PDE with nonlinear boundary conditions
• A numerical method for finding multiple co-existing solutions to nonlinear cooperative systems
• Blowup and solitary wave solutions with ring profiles of two-component nonlinear Schrödinger systems
• Minimax theorems
• Dual variational methods in critical point theory and applications
• A local minimax characterization for computing multiple nonsmooth saddle critical points
• A Minimax Method for Finding Multiple Critical Points and Its Applications to Semilinear PDEs
• An orthogonal subspace minimization method for finding multiple solutions to the defocusing nonlinear Schrödinger equation with symmetry
• On Finding Multiple Solutions to a Singularly Perturbed Neumann Problem
• Global Sequence Convergence of a Local Minimax Method for Finding Multiple Solutions in Banach Spaces
• A local min-max-orthogonal method for finding multiple solutions to noncooperative elliptic systems
• Unified Convergence Results on a Minimax Algorithm for Finding Multiple Critical Points in Banach Spaces
• Numerical Methods for Computing Nonlinear Eigenpairs: Part I. Iso-Homogeneous Cases
• Numerical Methods for Computing Nonlinear Eigenpairs: Part II. Non-Iso-Homogeneous Cases
• Remarks on finding critical points
• A high-linking algorithm for sign-changing solutions of semilinear elliptic equations
• Convergence Results of a Local Minimax Method for Finding Multiple Critical Points
• A mountain pass method for the numerical solution of semilinear elliptic problems
• A Minimax Method for Finding Multiple Critical Points in Banach Spaces and Its Application to Quasi-linear Elliptic PDE
• A minimax method for finding saddle critical points of upper semi-differentiable locally Lipschitz continuous functional in Hilbert space and its convergence

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