\(hp\) optimization of finite element approximations: Analysis of the optimal mesh sequences in one dimension

DOI10.1016/S0045-7825(97)00100-XzbMath0908.65073OpenAlexW2129921129MaRDI QIDQ1267861

K. Copps, Theofanis Strouboulis, Ivo M. Babuška

Publication date: 13 October 1998

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(97)00100-x

zbMATH Keywords

error boundssingular solutionexponential rate of convergenceadaptive \(hp\) finite element methodfeedback algorithmoptimal \(hp\) meshes

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (6)

An \(hpr\)-mesh refinement algorithm for BEM ⋮ A goal-oriented anisotropic \(hp\)-mesh adaptation method for linear convection-diffusion-reaction problems ⋮ \(hp\)-discontinuous Galerkin method based on local higher order reconstruction ⋮ Generalized boundary element method for Galerkin boundary integrals ⋮ A \(p\)-adaptive scaled boundary finite element method based on maximization of the error decrease rate ⋮ A fast \(hp\) adaptive finite element mesh design

Cites Work

• Toward a universal h-p adaptive finite element strategy. III: Design of h-p meshes
• Feedback and adaptive finite element solution of one-dimensional boundary value problems
• The h, p and h-p versions of the finite element method in 1 dimension. III. The adaptive h-p version

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