A systematic strategy for simultaneous adaptive \(hp\) finite element mesh modification using nonlinear programming

DOI10.1016/S0045-7825(00)00298-XzbMath0990.65133OpenAlexW2081401616MaRDI QIDQ5938292

Abani Patra, Ashish Gupta

Publication date: 18 July 2002

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(00)00298-x

zbMATH Keywords

algorithmfinite element methodnonlinear programming\(hp\)-adaptive mesh refinementa priori error estimatesoptimal mesh designoptimization problemPoisson problem

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Applications of mathematical programming (90C90) Nonlinear programming (90C30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items

Learning Robust Marking Policies for Adaptive Mesh Refinement ⋮ Data structures and load balancing for parallel adaptive \(hp\) finite-element methods ⋮ A Comparison of hp -Adaptive Strategies for Elliptic Partial Differential Equations

Uses Software

• MINOS

Cites Work

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• A unified approach to a posteriori error estimation using element residual methods
• The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version
• A parallel adaptive strategy for \(hp\) finite element computations
• The $h-p$ version of the finite element method with quasiuniform meshes
• hp‐version discontinuous Galerkin methods for hyperbolic conservation laws: A parallel adaptive strategy