A shadowing result with applications to finite element approximation of reaction-diffusion equations

DOI10.1090/S0025-5718-99-01038-8zbMath0913.65079OpenAlexW2074813764WikidataQ59593899 ScholiaQ59593899MaRDI QIDQ4221968

Stig Larsson, Jesús María Sanz-Serna

Publication date: 3 December 1998

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01038-8

zbMATH Keywords

finite element methoderror boundsdynamical systemerror estimatereaction-diffusion equationsshadowingsemilinear parabolic problembackward Eulerhyperbolic stationary point

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items

The exponential dichotomy on general approximation scheme ⋮ Approximation of semilinear fractional Cauchy problem. II ⋮ On approximate solutions for a class of semilinear fractional-order differential equations in Banach spaces ⋮ Solution of lambda-omega systems: Theta-schemes and multigrid methods ⋮ Dynamics of parabolic equations via the finite element method. I: Continuity of the set of equilibria. ⋮ Persistence of invariant sets for dissipative evolution equations ⋮ A General Approximation Scheme for Attractors of Abstract Parabolic Problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• Rigorous computational shadowing of orbits of ordinary differential equations
• On the Numerical Approximation of Phase Portraits Near Stationary Points
• The Stability in L p and W p 1 of the L 2 -Projection onto Finite Element Function Spaces
• On the qualitative behavior of the orbits of a parabolic partial differential equation and its discretization in the neighborhood of a hyperbolic fixed point
• Error Estimates with Smooth and Nonsmooth Data for a Finite Element Method for the Cahn-Hilliard Equation
• The Behavior of Finite Element Solutions of Semilinear Parabolic Problems Near Stationary Points
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms