An Optimal Adaptive Finite Element Method

DOI10.1137/S0036142903425082zbMath1081.65112MaRDI QIDQ5698740

Publication date: 28 October 2005

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

convergence Dirichlet problem discontinuous coefficients adaptive finite element methods a posteriori error estimator second-order elliptic equation optimal computational complexity quasi-optimization disconinuous coefficients quasi-wavelet basis

Mathematics Subject Classification ID

[https%3A%2F%2Fportal.mardi4nfdi.de%2Fw%2Findex.php%3Ftitle%3D%2BSpecial%253ASearch%26search%3DBoundary+value+problems+for+second-order+elliptic+equations%26go%3DGo Boundary value problems for second-order elliptic equations (35J25)] [https%3A%2F%2Fportal.mardi4nfdi.de%2Fw%2Findex.php%3Ftitle%3D%2BSpecial%253ASearch%26search%3DError+bounds+for+boundary+value+problems+involving+PDEs%26go%3DGo Error bounds for boundary value problems involving PDEs (65N15)] [https%3A%2F%2Fportal.mardi4nfdi.de%2Fw%2Findex.php%3Ftitle%3D%2BSpecial%253ASearch%26search%3DStability+and+convergence+of+numerical+methods+for+boundary+value+problems+involving+PDEs%26go%3DGo Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12)] [https%3A%2F%2Fportal.mardi4nfdi.de%2Fw%2Findex.php%3Ftitle%3D%2BSpecial%253ASearch%26search%3DFinite+element%2C+Rayleigh-Ritz+and+Galerkin+methods+for+boundary+value+problems+involving+PDEs%26go%3DGo Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)] [https%3A%2F%2Fportal.mardi4nfdi.de%2Fw%2Findex.php%3Ftitle%3D%2BSpecial%253ASearch%26search%3DNumerical+methods+for+wavelets%26go%3DGo Numerical methods for wavelets (65T60)] [https%3A%2F%2Fportal.mardi4nfdi.de%2Fw%2Findex.php%3Ftitle%3D%2BSpecial%253ASearch%26search%3DPDEs+with+low+regular+coefficients+and%2For+low+regular+data%26go%3DGo PDEs with low regular coefficients and/or low regular data (35R05)] [https%3A%2F%2Fportal.mardi4nfdi.de%2Fw%2Findex.php%3Ftitle%3D%2BSpecial%253ASearch%26search%3DMesh+generation%2C+refinement%2C+and+adaptive+methods+for+boundary+value+problems+involving+PDEs%26go%3DGo Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)] [https%3A%2F%2Fportal.mardi4nfdi.de%2Fw%2Findex.php%3Ftitle%3D%2BSpecial%253ASearch%26search%3DComplexity+and+performance+of+numerical+algorithms%26go%3DGo Complexity and performance of numerical algorithms (65Y20)]

Related Items (25)

Adaptive Finite Element Approximations for Elliptic Problems using Regularized Forcing Data ⋮ Projection in negative norms and the regularization of rough linear functionals ⋮ Quasi-optimality of adaptive finite element methods for controlling local energy errors ⋮ Convergence Rates for Adaptive Weak Approximation of Stochastic Differential Equations ⋮ An adaptive \(hp\)-refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor ⋮ Convergence rates of AFEM with \(H^{-1}\) data ⋮ Saturation estimates for \(hp\)-finite element methods ⋮ Guaranteed contraction of adaptive inexact hp-refinement strategies with realistic stopping criteria ⋮ Convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problem ⋮ Convergence of adaptive boundary element methods ⋮ On adaptive Eulerian-Lagrangian method for linear convection-diffusion problems ⋮ Adaptive multiresolution analysis based on anisotropic triangulations ⋮ Convergence analysis of a conforming adaptive finite element method for an obstacle problem ⋮ Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation ⋮ Simplicial finite elements in higher dimensions. ⋮ An optimally convergent adaptive mixed finite element method ⋮ Adaptive frame methods for nonlinear variational problems ⋮ A posteriori error estimator and error control for contact problems ⋮ Convergence rates for an adaptive dual weighted residual finite element algorithm ⋮ A posteriori error analysis for finite element solution of one-dimensional elliptic differential equations using equidistributing meshes ⋮ A stopping criterion for the conjugate gradient algorithm in the framework of anisotropic adaptive finite elements ⋮ Further results on error estimators for local refinement with first-order system least squares (FOSLS) ⋮ Variationally consistent discretization schemes and numerical algorithms for contact problems ⋮ Wavelet Galerkin Methods for Higher Order Partial Differential Equations ⋮ The uniform saturation property for a singularly perturbed reaction-diffusion equation

This page was built for publication: An Optimal Adaptive Finite Element Method