An efficient Legendre-Galerkin approximation for the fourth-order equation with singular potential and SSP boundary condition
DOI10.1515/MATH-2023-0128zbMATH Open1547.65183MaRDI QIDQ6611474
Publication date: 26 September 2024
Published in: Open Mathematics (Search for Journal in Brave)
error estimationsingular potentialfourth-order equationLegendre-Galerkin approximationSSP boundary condition
Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Eigenvalues, singular values, and eigenvectors (15A18) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
- Title not available (Why is that?)
- A posteriori eigenvalue error estimation for a Schrödinger operator with inverse square potential
- A posteriori error estimation of hierarchical type for the Schrödinger operator with inverse square potential
- Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential
- Error estimates of spectral Legendre-Galerkin methods for the fourth-order equation in one dimension
- Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials
- On the behavior of solutions to Schrödinger equations with dipole type potentials near the singularity
- The scalar auxiliary variable (SAV) approach for gradient flows
- Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
- Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem
- Galerkin spectral approximations for optimal control problems governed by the fourth order equation with an integral constraint on state
- A novel numerical method based on a high order polynomial approximation of the fourth order Steklov equation and its eigenvalue problems
- Spectral approximation based on a mixed scheme and its error estimates for transmission eigenvalue problems
- An efficient spectral-Galerkin approximation based on dimension reduction scheme for transmission eigenvalues in polar geometries
- Analysis of a modified Schrödinger operator in 2D: Regularity, index, and FEM
- A Legendre spectral Galerkin method for the biharmonic Dirichlet problem
- Efficient Spectral and Spectral Element Methods for Eigenvalue Problems of Schrödinger Equations with an Inverse Square Potential
- Spectral Methods
- A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods
- Finite-Difference Approximations to Singular Sturm-Liouville Eigenvalue Problems
- Timely Communication: Efficient Algorithms for Solving a Fourth-Order Equation with the Spectral-Galerkin Method
- Efficient Spectral-Galerkin Methods III: Polar and Cylindrical Geometries
- Discrete-Time Orthogonal Spline Collocation Methods for Vibration Problems
- Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint
- An efficient finite-element method and error analysis for the fourth-order elliptic equation in a circular domain
- Numerical Analysis of an Optimal Control Problem Governed by the Stationary Navier-Stokes Equations with Global Velocity-Constrained
- A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
- Analysis of Schr\"odinger operators with inverse square potentials I: regularity results in 3D
- Highly Efficient and Accurate Spectral Approximation of the Angular Mathieu Equation for any Parameter Values q
- An efficient spectral method and rigorous error analysis based on dimension reduction scheme for fourth order problems
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