The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. I: Superconvergence error analysis
DOI10.1007/s10915-013-9782-0zbMath1297.74112OpenAlexW2016112718WikidataQ115382696 ScholiaQ115382696MaRDI QIDQ461268
Publication date: 10 October 2014
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-013-9782-0
stabilityprojectionsuperconvergenceoptimal error estimateslocal discontinuous Galerkin methodfourth-order Euler-Bernoulli equation
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs in connection with mechanics of deformable solids (35Q74)
Related Items (25)
Cites Work
- Unnamed Item
- Unnamed Item
- A local discontinuous Galerkin method for the second-order wave equation
- The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. II: A posteriori error estimation
- Superconvergence of discontinuous finite element solutions for transient convection-diffusion problems
- The discontinuous Galerkin method for two-dimensional hyperbolic problems. II: A posteriori error estimation
- Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes
- A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
- On fourth order boundary value problems arising in beam analysis
- A discontinuous Galerkin method for higher-order ordinary differential equations
- An efficient method for computing eigenelements of Sturm-Liouville fourth-order boundary value problems
- Positive solutions of fourth-order nonlinear singular Sturm--Liouville eigenvalue problems
- Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem
- Existence and uniqueness results for the bending of an elastic beam equation at resonance
- TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
- A discontinuous \(hp\) finite element method for convection-diffusion problems
- Parallel, adaptive finite element methods for conservation laws
- A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
- \(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws
- A superconvergence result for discontinuous Galerkin methods applied to elliptic problems.
- A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems.
- A parallel \(hp\)-adaptive discontinuous Galerkin method for hyperbolic conservation laws
- Parallel adaptive \(hp\)-refinement techniques for conservation laws
- A superconvergent local discontinuous Galerkin method for elliptic problems
- Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24--26, 1999
- The discontinuous Galerkin method for two-dimensional hyperbolic problems. I: Superconvergence error analysis
- A posteriori local discontinuous Galerkin error estimation for two-dimensional convection-diffusion problems
- An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
- Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
- Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension
- Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension
- Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations
- TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
- Discontinuous Galerkin Methods for Ordinary Differential Equations
- An Elliptic Collocation-Finite Element Method with Interior Penalties
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Superconvergence of the local discontinuous Galerkin method for linear fourth-order time-dependent problems in one space dimension
- Oscillation theory and numerical solution of fourth-order Sturm—Liouville problems
- hp‐version discontinuous Galerkin methods for hyperbolic conservation laws: A parallel adaptive strategy
This page was built for publication: The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. I: Superconvergence error analysis