Optimally accurate higher-order finite element methods for polytopial approximations of domains with smooth boundaries

DOI10.1090/mcom/3415zbMath1417.65186arXiv1710.05628OpenAlexW2964135693WikidataQ128453293 ScholiaQ128453293MaRDI QIDQ5380091

James Cheung, Mauro Perego, Max D. Gunzburger, Pavel B. Bochev

Publication date: 14 June 2019

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

Full work available at URL: https://arxiv.org/abs/1710.05628

zbMATH Keywords

curved boundarieshigher-order finite element methods

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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

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Cites Work

• Unnamed Item
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• Solving convection-diffusion problems on curved domains by extensions from subdomains
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• Least-squares finite element methods
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Finite element approximation of the Dirichlet problem using the boundary penalty method
• Theory and practice of finite elements.
• The shifted boundary method for embedded domain computations. I: Poisson and Stokes problems
• The shifted boundary method for embedded domain computations. II: Linear advection-diffusion and incompressible Navier-Stokes equations
• Curved, isoparametric, 'quadrilateral' elements for finite element analysis
• Interpolation theory over curved elements, with applications to finite element methods
• High-order accurate implementation of solid wall boundary conditions in curved geometries
• A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity
• Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains
• 3D NURBS-enhanced finite element method (NEFEM)
• Optimal Isoparametric Finite Elements and Error Estimates for Domains Involving Curved Boundaries
• A cut finite element method with boundary value correction
• Isogeometric Analysis
• Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting
• Accuracy and condition of curved (isoparametric) finite elements
• The Virtual Element Method with curved edges
• A New Finite Element Gradient Recovery Method: Superconvergence Property
• The Mathematical Theory of Finite Element Methods