On optimal convergence rate of finite element solutions of boundary value problems on adaptive anisotropic meshes

DOI10.1016/j.matcom.2010.12.027zbMath1221.65291OpenAlexW2035445279MaRDI QIDQ554519

Yuri V. Vassilevski, Abdellatif Agouzal, Konstantin N. Lipnikov

Publication date: 4 August 2011

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2010.12.027

zbMATH Keywords

convergencefinite element methodnumerical examplesestimatesNavier-Stokes equationStokes equationlinear isotropic diffusion equationmetric-based adaptationnonlinear transonic potential equationquasi-optimal meshes

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Navier-Stokes equations for incompressible viscous fluids (76D05) Transonic flows (76H05) Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) 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) Navier-Stokes equations (35Q30) Finite element methods applied to problems in fluid mechanics (76M10) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

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Cites Work

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• Minimization of gradient errors of piecewise linear interpolation on simplicial meshes
• A finite volume method for advection-diffusion problems in convection-dominated regimes
• Anisotropic error estimates for elliptic problems
• Parallel adaptive solution of 3D boundary value problems by Hessian recovery
• An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes
• Metric tensors for anisotropic mesh generation
• Unified asymptotic analysis of interpolation errors for optimal meshes
• Hessian-free metric-based mesh adaptation via geometry of interpolation error
• Finite elements for transonic potential flows
• Concepts of an adaptive hierarchical finite element code
• Optimal Triangular Mesh Generation by Coordinate Transformation
• An adaptive algorithm for quasioptimal mesh generation