Convergence and quasi-optimality of an adaptive finite element method for nonmonotone quasi-linear elliptic problems on \(L^2\) errors
DOI10.1016/j.camwa.2023.03.005OpenAlexW4327546956MaRDI QIDQ6161530
Publication date: 5 June 2023
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2023.03.005
convergenceadaptive finite element methodquasi-optimality\( L^2\) errorsnonmonotone elliptic problems
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)
Cites Work
- Unnamed Item
- Unnamed Item
- A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems
- Quasi-optimal convergence rate of an adaptive weakly over-penalized interior penalty method
- Adaptive finite element method for elliptic optimal control problems: convergence and optimality
- Convergence and quasi-optimality of an adaptive finite element method for controlling \(L_{2}\) errors
- An optimally convergent adaptive mixed finite element method
- Convergence of a standard adaptive nonconforming finite element method with optimal complexity
- On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type
- Uniqueness of discrete solutions of nonmonotone PDEs without a globally fine mesh condition
- Convergence and quasi-optimality of an adaptive finite element method for optimal control problems on \(L^{2}\) errors
- Adaptive finite element methods with convergence rates
- A posteriori error estimates of discontinuous Galerkin method for nonmonotone quasi-linear elliptic problems
- The finite volume method for Richards equation
- Two-grid finite element method and its a posteriori error estimates for a nonmonotone quasilinear elliptic problem under minimal regularity of data
- Adaptive finite element method for nonmonotone quasi-linear elliptic problems
- Adaptive least-squares finite element methods for linear transport equations based on an H(div) flux reformulation
- Convergence and quasi-optimality of \(L^2\)-norms based an adaptive finite element method for nonlinear optimal control problems
- Optimality of a standard adaptive finite element method
- Two-grid finite-element schemes for the transient Navier-Stokes problem
- Optimality of an adaptive finite element method for the p-Laplacian equation
- A Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity
- Quasi-Optimality of Adaptive Nonconforming Finite Element Methods for the Stokes Equations
- ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- A BASIC CONVERGENCE RESULT FOR CONFORMING ADAPTIVE FINITE ELEMENTS
- Theory of adaptive finite element methods: An introduction
- Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
- Convergence and quasi-optimal complexity of a simple adaptive finite element method
- Global Superconvergence and A Posteriori Error Estimators of the Finite Element Method for a Quasi-linear Elliptic Boundary Value Problem of Nonmonotone Type
- A Convergent Adaptive Algorithm for Poisson’s Equation
- Quasi-Optimal Convergence Rate of an AFEM for Quasi-Linear Problems of Monotone Type
- Convergence and quasi-optimality of an adaptive finite element method for semilinear elliptic problems on L2 errors
- Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs
- Adaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems
