A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations
From MaRDI portal
Publication:4326862
DOI10.1137/0732001zbMath0820.65052OpenAlexW2081416965MaRDI QIDQ4326862
Publication date: 27 March 1995
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0732001
error boundsinitial value problemsstiff problemstest problemsadaptive error controlsuperstabilitydiscontinuous Galerkin finite element methodglobal error controldiscrete Gronwall inequalitydissipative problemscontractive problemsknee problem
Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)
Related Items
A posteriori analysis of an IMEX entropy-viscosity formulation for hyperbolic conservation laws with dissipation, Adaptive weak approximation of stochastic differential equations, Analysis of a posteriori error estimates of the discontinuous Galerkin method for nonlinear ordinary differential equations, The dynamical behavior of the discontinuous Galerkin method and related difference schemes, 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, A Posteriori Error Estimates for the Solution of Variational Inverse Problems, Error Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertainty, Unnamed Item, A posteriori error estimation for multi-stage Runge-Kutta IMEX schemes, Error estimation and adaptation for functional outputs in time-dependent flow problems, A posteriori error estimates and adaptivity for the discontinuous Galerkin solutions of nonlinear second-order initial-value problems, A Superconvergent discontinuous Galerkin method for Volterra integro-differential equations, smooth and non-smooth kernels, Error estimation and uncertainty quantification for first time to a threshold value, A posteriori error analysis of fluid-structure interactions: time dependent error, A posteriori error analysis of round-off errors in the numerical solution of ordinary differential equations, A posteriori error analysis for Schwarz overlapping domain decomposition methods, Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods, A Posteriori Analysis and Efficient Refinement Strategies for the Poisson--Boltzmann Equation, The ROMES Method for Statistical Modeling of Reduced-Order-Model Error, A Posteriori Analysis for Iterative Solvers for Nonautonomous Evolution Problems, Continuous and discontinuous Galerkin time stepping methods for nonlinear initial value problems with application to finite time blow-up, Adaptiveh-refinement for reduced-order models, On the development of symmetry-preserving finite element schemes for ordinary differential equations, Error estimation for the time to a threshold value in evolutionary partial differential equations, \textit{A posteriori} error estimation for the spectral deferred correction method, A posteriori discontinuous Galerkin error estimation on tetrahedral meshes, Accounting for stability: a posteriori error estimates based on residuals and variational analysis, A posteriori error estimation of approximate boundary fluxes, A posteriori error analysis for finite element methods with projection operators as applied to explicit time integration techniques, A posteriori error analysis for higher order dissipative methods for evolution problems, A new approach to estimating a numerical solution in the error embedded correction framework, A superconvergent discontinuous Galerkin method for hyperbolic problems on tetrahedral meshes, The \(hp\)- and \(h\)-versions of the discontinuous and local discontinuous Galerkin methods for one-dimensional singularly perturbed models, Multi-adaptive time integration., \textit{A posteriori} analysis of an iterative multi-discretization method for reaction-diffusion systems, \(L^\infty\) error estimates of discontinuous Galerkin methods for delay differential equations, Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: definition and outlook, Truncation error estimation in the p-anisotropic discontinuous Galerkin spectral element method, Towards efficient backward-in-time adjoint computations using data compression techniques, Goal-oriented adaptive surrogate construction for stochastic inversion, A discontinuous finite element approximation to singular Lane-Emden type equations, \(hp\)-adaptive Galerkin time stepping methods for nonlinear initial value problems, Superconvergence of the discontinuous Galerkin method for nonlinear second-order initial-value problems for ordinary differential equations, Explicit a-priori error bounds and adaptive error control for approximation of nonlinear initial value differential systems, A posteriori error estimation for the Lax-Wendroff finite difference scheme, A unified discontinuous Galerkin framework for time integration, Nonlinear stability of discontinuous Galerkin methods for delay differential equations, 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, Fast and reliable methods for determining the evolution of uncertain parameters in differential equations, On the geometric conservation law for high-order discontinuous Galerkin discretizations on dynamically deforming meshes, A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid-solid heat transfer, An \textit{a priori} error analysis of the \(hp\)-version of the continuous Galerkin FEM for nonlinear initial value problems, The solution of a launch vehicle trajectory problem by an adaptive finite element method, A posteriori error estimation and adaptivity in the method of lines with mixed finite elements., Estimating spatial and parameter error in parameterized nonlinear reaction–diffusion equations, On a new reliable modification of homotopy analysis method, Pointwise error estimation and adaptivity for the finite element method using fundamental solutions, Goal-oriented error estimation for beams on elastic foundation with double shear effect, Goal-oriented error estimation in the analysis of fluid flows with structural interactions, Quantifying uncertainty in material damage from vibrational data, A posteriorierror analysis of a cell-centered finite volume method for semilinear elliptic problems, Adjoint-based \(h\)-\(p\) adaptive discontinuous Galerkin methods for the 2D compressible Euler equations, A posteriori error analysis of IMEX multi-step time integration methods for advection-diffusion-reaction equations, Global error control for the continuous Galerkin finite element method for ordinary differential equations, Strict upper and lower bounds for quantities of interest in static response sensitivity analysis, Variational time discretizations of higher order and higher regularity, Global dynamics of target-mediated drug disposition models and their solutions by nonstandard finite difference method, An adjoint-based a posteriori analysis of numerical approximation of Richards equation, Applications and numerical analysis of partial differential Volterra equations: A brief survey, A role for symmetry in the Bayesian solution of differential equations, A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm, A p-multigrid strategy with anisotropic p-adaptation based on truncation errors for high-order discontinuous Galerkin methods, Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems, Fast methods for determining the evolution of uncertain parameters in reaction-diffusion equations, A posteriori error estimates for space-time finite element approximation of quasistatic hereditary linear viscoelasticity problems, Discontinuous Galerkin time discretization methods for parabolic problems with linear constraints, Conditional A Posteriori Error Bounds for High Order Discontinuous Galerkin Time Stepping Approximations of Semilinear Heat Models with Blow-up
