Incomplete Iterations in Multistep Backward Difference Methods for Parabolic Problems with Smooth and Nonsmooth Data

DOI10.2307/2008471zbMath0663.65110OpenAlexW4237144600MaRDI QIDQ3814723

Joseph E. Pasciak, James H. Bramble, Vidar Thomée, P. H. Sammon

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2008471

zbMATH Keywords

numerical experimentsconjugate gradient methodimplicit multistep backward difference methodsincomplete iterationspreconditional iteration

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Iterative numerical methods for linear systems (65F10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (19)

Stabilized explicit Runge-Kutta methods for multi-asset American options ⋮ An ETD Crank-Nicolson method for reaction-diffusion systems ⋮ Edge-forming methods for image zooming ⋮ A posteriori error analysis of two-step backward differentiation formula finite element approximation for parabolic interface problems ⋮ A block-matrix iterative numerical method for coupled solving 2D Navier- Stokes equations ⋮ A symmetric characteristic FVE method with second order accuracy for nonlinear convection diffusion problems ⋮ Incomplete iterative implicit schemes ⋮ The expanded upwind-mixed multi-step method for the miscible displacement problem in three dimensions ⋮ Smoothing schemes for reaction-diffusion systems with nonsmooth data ⋮ Solution of lambda-omega systems: Theta-schemes and multigrid methods ⋮ Smoothing with positivity-preserving Padé schemes for parabolic problems with nonsmooth data ⋮ Two-scale composite finite element method for parabolic problems with smooth and nonsmooth initial data ⋮ A three level finite element approximation of a pattern formation model in developmental biology ⋮ Cascadic multigrid methods for parabolic problems ⋮ Multigrid methods for time-fractional evolution equations: a numerical study ⋮ A variational formulation of the BDF2 method for metric gradient flows ⋮ Error estimates for two-scale composite finite element approximations of parabolic equations with measure data in time for convex and nonconvex polygonal domains ⋮ A second order backward difference method with variable steps for a parabolic problem ⋮ Incomplete iterative solution of subdiffusion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Erratum: On the multi-level splitting of finite element spaces
• A preconditioning technique for the efficient solution of problems with local grid refinement
• Discrete time Galerkin methods for a parabolic boundary value problem
• Iterative methods for the solution of a linear operator equation in Hilbert space. A survey
• Semidiscretization in Time for Parabolic Problems
• The Construction of Preconditioners for Elliptic Problems by Substructuring, III
• An Iterative Method for Elliptic Problems on Regions Partitioned into Substructures
• The Construction of Preconditioners for Elliptic Problems by Substructuring. II
• New Convergence Estimates for Multigrid Algorithms
• The Construction of Preconditioners for Elliptic Problems by Substructuring, IV
• Galerkin/Runge-Kutta Discretizations for Parabolic Equations with Time- Dependent Coefficients
• Efficient Higher Order Single Step Methods for Parabolic Problems: Part I
• Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations
• Single Step Galerkin Approximations for Parabolic Problems
• Incomplete Iteration for Time-Stepping a Galerkin Method for a Quasilinear Parabolic Problem
• The Construction of Preconditioners for Elliptic Problems by Substructuring. I
• An Approximate Factorization Procedure for Solving Self-Adjoint Elliptic Difference Equations
• On the instability of high order backward-difference multistep methods

This page was built for publication: Incomplete Iterations in Multistep Backward Difference Methods for Parabolic Problems with Smooth and Nonsmooth Data