Robust error estimation in energy and balanced norms for singularly perturbed fourth order problems

DOI10.1016/j.camwa.2016.05.001zbMath1443.74221OpenAlexW2395329040MaRDI QIDQ2007315

Hans-Goerg Roos, Sebastian Franz

Publication date: 12 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2016.05.001

zbMATH Keywords

singular perturbationboundary layerslayer-adapted meshesfourth-order problembalanced normsmixed-method

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Boundary value problems for higher-order elliptic equations (35J40) Plates (74K20)

Related Items (12)

On the finite element approximation of fourth-order singularly perturbed eigenvalue problems ⋮ Asymptotic Analysis and a Uniformly Convergent Numerical Method for Singular Perturbation Problems ⋮ An \(hp\) finite element method for a 4th order singularly perturbed boundary value problem in two dimensions ⋮ Solving a singular beam equation by the method of energy boundary functions ⋮ The Bogner-Fox-Schmit element finite volume methods on the Shishkin mesh for fourth-order singularly perturbed elliptic problems ⋮ Mixed hp finite element method for singularly perturbed fourth order boundary value problems with two small parameters ⋮ Uniformly convergent scheme for fourth-order singularly perturbed convection-diffusion ODE ⋮ Local discontinuous Galerkin method for a singularly perturbed fourth-order problem of reaction-diffusion type ⋮ A parameter robust finite element method for fourth order singularly perturbed problems ⋮ Convergence analysis of the Adini element on a Shishkin mesh for a singularly perturbed fourth-order problem in two dimensions ⋮ A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains ⋮ Numerical treatment of singularly perturbed fourth-order two-parameter problems

Cites Work

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• A \(C^{1}\)-conforming \(hp\) finite element method for fourth order singularly perturbed boundary value problems
• Comparing hinged and supported rectangular plates
• A family of non-conforming elements and the analysis of Nitsche's method for a singularly perturbed fourth order problem
• Local projection stabilisation for higher order discretisations of convection-diffusion problems on Shishkin meshes
• Full-order convergence of a mixed finite element method for fourth-order elliptic equations
• L ∞ -Bounds for the L 2-Projection onto Linear Spline Spaces
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Finite Element Methods for Navier-Stokes Equations
• A Mixed Finite Element Method for the Biharmonic Equation
• On the boundary value problem of the biharmonic operator on domains with angular corners
• Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems
• A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems
• A C⁰ interior penalty method for a singularly‐perturbed fourth‐order elliptic problem on a layer‐adapted mesh

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