Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems
DOI10.1007/s00211-010-0307-6zbMath1201.65195OpenAlexW2043379273MaRDI QIDQ707578
Huangxin Chen, Ronald H. W. Hoppe, Xuejun Xu
Publication date: 8 October 2010
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00211-010-0307-6
convergencenumerical experimentsadaptive finite element methoda posteriori estimatesnonconformingquasi-optimalitynonsymmetric and indefinite elliptic boundary value problem
Boundary value problems for second-order elliptic equations (35J25) 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) Complexity and performance of numerical algorithms (65Y20)
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- Intergrid transfer operators and multilevel preconditioners for nonconforming discretizations
- An \(H^S\)-regularity result for the gradient of solutions to elliptic equations with mixed boundary conditions
- Adaptive finite element methods for elliptic equations with non-smooth coefficients
- Elliptic partial differential equations of second order
- A posteriori error estimates for nonconforming finite element methods
- Adaptive finite element methods with convergence rates
- Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions
- Convergence and domain decomposition algorithm for nonconforming and mixed methods for nonselfadjoint and indefinite problems
- A unifying theory of a posteriori error control for nonconforming finite element methods
- Optimality of a standard adaptive finite element method
- Convergence analysis of an adaptive nonconforming finite element method
- Convergence and optimality of adaptive mixed finite element methods
- A Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity
- Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
- An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
- Multigrid Algorithms for Nonconforming and Mixed Methods for Nonsymmetric and Indefinite Problems
- A posterioriError Estimates with Post-Processing for Nonconforming Finite Elements
- Poincaré--Friedrichs Inequalities for Piecewise H1 Functions
- On the Efficiency of Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
- Convergence of Adaptive Finite Element Methods
- On the Implementation of Mixed Methods as Nonconforming Methods for Second- Order Elliptic Problems
- Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
- Some new error estimates for Ritz–Galerkin methods with minimal regularity assumptions
- A posteriori error estimators for nonconforming finite element methods
- Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods
- Elliptic Differential Equations
- Framework for the A Posteriori Error Analysis of Nonconforming Finite Elements
- Error reduction and convergence for an adaptive mixed finite element method
- Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs
- Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation
- Three Matlab Implementations of the Lowest-order Raviart-Thomas Mfem with a Posteriori Error Control
- A posteriori error estimators for elliptic equations with discontinuous coefficients
