Postprocessing Fourier spectral methods: the case of smooth solutions
Applied Numerical Mathematics
Generating Minimal Surfaces Subject to the Plateau Problems by Finite Element Method
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Global and uniform convergence of subspace correction methods for some convex optimization problems
Mathematics of Computation
Finite element approximation for the viscoelastic fluid motion problem
Journal of Computational and Applied Mathematics
The finite element approximation for minimal surfaces subject to the plateau problems
ICCST '02 Proceedings of the sixth conference on Computational structures technology
On monotone iteration and Schwarz methods for nonlinear parabolic PDEs
Journal of Computational and Applied Mathematics
Some new discretization and adaptation and multigrid methods for 2-D 3-T diffusion equations
Journal of Computational Physics
A two-grid method based on Newton iteration for the Navier-Stokes equations
Journal of Computational and Applied Mathematics
Two-grid methods for finite volume element approximations of nonlinear parabolic equations
Journal of Computational and Applied Mathematics
Two-level Galerkin-Lagrange multipliers method for the stationary Navier-Stokes equations
Journal of Computational and Applied Mathematics
Two-grid finite volume element methods for semilinear parabolic problems
Applied Numerical Mathematics
Discretization of the Navier-Stokes equationswith slip boundary condition II
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Newton Iterative Parallel Finite Element Algorithm for the Steady Navier-Stokes Equations
Journal of Scientific Computing
Finite Elements in Analysis and Design
A new parallel finite element algorithm for the stationary Navier-Stokes equations
Finite Elements in Analysis and Design
Convergence of a FEM and two-grid algorithms for elliptic problems on disjoint domains
Journal of Computational and Applied Mathematics
A cascadic multigrid method for a kind of semilinear elliptic problem
Numerical Algorithms
Two-Grid Method for Nonlinear Reaction-Diffusion Equations by Mixed Finite Element Methods
Journal of Scientific Computing
Two-Grid Discontinuous Galerkin Method for Quasi-Linear Elliptic Problems
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
Postprocessed Two-Scale Finite Element Discretizations, Part I
SIAM Journal on Numerical Analysis
Error estimates of the lumped mass finite element method for semilinear elliptic problems
Journal of Computational and Applied Mathematics
A multilevel decoupled method for a mixed Stokes/Darcy model
Journal of Computational and Applied Mathematics
HPCA'09 Proceedings of the Second international conference on High Performance Computing and Applications
Two-Grid decoupling method for elliptic problems on disjoint domains
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Two-level stabilized method based on three corrections for the stationary Navier-Stokes equations
Applied Numerical Mathematics
Computers & Mathematics with Applications
Some iterative finite element methods for steady Navier-Stokes equations with different viscosities
Journal of Computational Physics
A two-level subgrid stabilized Oseen iterative method for the steady Navier-Stokes equations
Journal of Computational Physics
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Two-Level Newton's Method for Nonlinear Elliptic PDEs
Journal of Scientific Computing
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A number of finite element discretization techniques based on two (or more) subspaces for nonlinear elliptic partial differential equations (PDEs) is presented. Convergence estimates are derived to justify the efficiency of these algorithms. With the new proposed techniques, solving a large class of nonlinear elliptic boundary value problems will not be much more difficult than the solution of one linearized equation. Similar techniques are also used to solve nonsymmetric and/or indefinite linear systems by solving symmetric positive definite (SPD) systems. For the analysis of these two-grid or multigrid methods, optimal ${\cal L}^p$ error estimates are also obtained for the classic finite element discretizations.