Global error control for the continuous Galerkin finite element method for ordinary differential equations
From MaRDI portal
Publication:4698859
DOI10.1051/m2an/1994280708151zbMath0822.65054OpenAlexW2519750562MaRDI QIDQ4698859
Donald A. French, Donald J. Estep
Publication date: 15 October 1995
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/193761
Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70)
Related Items
Generalized Petrov-Galerkin time finite element weighted residual methodology for designing high-order unconditionally stable algorithms with controllable numerical dissipation, Discrete conservation laws for finite element discretisations of multisymplectic PDEs, ERROR GROWTH AND A POSTERIORI ERROR ESTIMATES FOR CONSERVATIVE GALERKIN APPROXIMATIONS OF PERIODIC ORBITS IN HAMILTONIAN SYSTEMS, Error Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertainty, Interior a posteriori error estimates for time discrete approximations of parabolic problems, The rate of error growth in Hamiltonian-conserving integrators, Optimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methods, A posteriori error analysis of round-off errors in the numerical solution of ordinary differential equations, A note on a norm-preserving continuous Galerkin time stepping scheme, Continuous and discontinuous Galerkin time stepping methods for nonlinear initial value problems with application to finite time blow-up, Stabilized methods for compressible flows, On time integration error estimation and adaptive time stepping in structural dynamics, An \(hp\)-version of the \(C^0\)-continuous Petrov-Galerkin time stepping method for nonlinear second-order initial value problems, Superconvergent postprocessing of the continuous Galerkin time stepping method for nonlinear initial value problems with application to parabolic problems, On the development of symmetry-preserving finite element schemes for ordinary differential equations, Galerkin and Runge-Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence, Implementing biological hybrid systems: allowing composition and avoiding stiffness, An L∞-error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems, A robust finite element method for elastic vibration problems, Multi-adaptive time integration., An \(h\)-\(p\) Petrov-Galerkin finite element method for linear Volterra integro-differential equations, Stabilized shock hydrodynamics. I: A Lagrangian method, Automating the finite element method, \(hp\)-adaptive Galerkin time stepping methods for nonlinear initial value problems, A sparse grid space-time discretization scheme for parabolic problems, A posteriori analysis of a multirate numerical method for ordinary differential equations, Error estimates and adaptive finite element methods, The continuous Galerkin finite element methods for linear neutral delay differential equations, A posteriori error estimation for \(hp\)-version time-stepping methods for parabolic partial differential equations, The solution of a launch vehicle trajectory problem by an adaptive finite element method, On variational and symplectic time integrators for Hamiltonian systems, Variational time discretizations of higher order and higher regularity, A posteriori error estimates for the Crank–Nicolson method for parabolic equations, A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm, Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems, A posteriori error estimates for space-time finite element approximation of quasistatic hereditary linear viscoelasticity problems, Conditional A Posteriori Error Bounds for High Order Discontinuous Galerkin Time Stepping Approximations of Semilinear Heat Models with Blow-up, Spectral variational integrators
Cites Work
- Unnamed Item
- Unnamed Item
- Continuous finite element methods which preserve energy properties for nonlinear problems
- Numerical quadrature and solution of ordinary differential equations. A textbook for a beginning course in numerical analysis
- Adaptive Finite Element Methods for Parabolic Problems I: A Linear Model Problem
- Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations
- Long-time behaviour of arbitrary order continuous time Galerkin schemes for some one-dimensional phase transition problems
- A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations
- The dynamical behavior of the discontinuous Galerkin method and related difference schemes
- Error Estimates and Automatic Time Step Control for Nonlinear Parabolic Problems, I
- Adaptive Finite Element Methods for Parabolic Problems II: Optimal Error Estimates in $L_\infty L_2 $ and $L_\infty L_\infty $
- Adaptive Finite Element Methods for Parabolic Problems IV: Nonlinear Problems
- Adaptive Finite Element Methods for Parabolic Problems V: Long-Time Integration
