A GENERAL OUTPUT BOUND RESULT: APPLICATION TO DISCRETIZATION AND ITERATION ERROR ESTIMATION AND CONTROL

DOI10.1142/S0218202501001057zbMath1012.65110OpenAlexW2156592123MaRDI QIDQ4798881

Einar M. Rønquist, Anthony T. Patera

Publication date: 16 March 2003

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202501001057

zbMATH Keywords

numerical resultsLanczos methodpreconditioningfinite element methodsPoisson equationSchwarz domain decompositiona posteriori error estimationoutput boundsconjugate gradient iterion

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows ⋮ A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations ⋮ Estimating and localizing the algebraic and total numerical errors using flux reconstructions ⋮ A stopping criterion for the iterative solution of partial differential equations ⋮ Certified reduced basis methods for parametrized parabolic partial differential equations with non-affine source terms ⋮ A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations ⋮ Output bounds for reduced-order approximations of elliptic partial differential equations ⋮ COMPUTING HIGHLY ACCURATE SOLUTIONS OF A TUMOUR ANGIOGENESIS MODEL ⋮ A posteriori finite-element output bounds for the incompressible Navier-Stokes equations: Application to a natural convection problem ⋮ A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations ⋮ Strict bounding of quantities of interest in computations based on domain decomposition ⋮ Interplay between discretization and algebraic computation in adaptive numerical solutionof elliptic PDE problems

Cites Work

• A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations
• A unified approach to a posteriori error estimation using element residual methods
• Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods
• The computation of bounds for the norm of the error in the conjugate gradient algorithm
• A hierarchical duality approach to bounds for the outputs of partial differential equations
• Adaptive error control for multigrid finite element methods
• Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: The Helmholtz and Burgers equations
• A Taxonomy for Conjugate Gradient Methods
• Error Estimate Procedure in the Finite Element Method and Applications
• A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem
• Practical Three-Dimensional Aerodynamic Design and Optimization Using Unstructured Meshes
• A posteriori bounds for linear functional outputs of Crouzeix-Raviart finite element discretizations of the incompressible Stokes problem

This page was built for publication: A GENERAL OUTPUT BOUND RESULT: APPLICATION TO DISCRETIZATION AND ITERATION ERROR ESTIMATION AND CONTROL