Error estimate of a finite element method for an optimal control problem with corner singularity using the stress intensity factor

DOI10.1002/num.22824OpenAlexW3185234064WikidataQ115397304 ScholiaQ115397304MaRDI QIDQ6069459

Hyung-Chun Lee, Seokchan Kim

Publication date: 16 December 2023

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.22824

zbMATH Keywords

finite element methodcorner singularityPoisson equationoptimal control problemstress intensity factor

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDE constrained optimization (numerical aspects) (49M41) Transport equations (35Q49)

Cites Work

• Singularities in elliptic boundary value problems and elasticity and their connection with failure initiation.
• On finite element methods for elliptic equations on domains with corners
• A finite element method for computing accurate solutions for Poisson equations with corner singularities using the stress intensity factor
• On the use of singular functions with finite element approximations
• A finite element method using singular functions for Poisson equations: Mixed boundary conditions
• A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities
• Coefficients of the Singularities for Elliptic Boundary Value Problems on Domains with Conical Points. III: Finite Element Methods on Polygonal Domains
• Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities
• New development in freefem++
• Weighted‐Norm First‐Order System Least Squares (FOSLS) for Problems with Corner Singularities
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