Gradient-finite Element Method for Nonlinear Neumann Problems
نویسنده
چکیده
We consider the numerical solution of quasilinear elliptic Neumann problems. The basic difficulty is the non-injectivity of the operator, which can be overcome by suitable factorization. We extend the gradient-finite element method (GFEM), introduced earlier by the authors for Dirichlet problems, to the Neumann problem. The algorithm is constructed and its convergence is proved.
منابع مشابه
A New Stress Based Approach for Nonlinear Finite Element Analysis
This article demonstrates a new approach for nonlinear finite element analysis. The methodology is very suitable and gives very accurate results in linear as well as in nonlinear range of the material behavior. Proposed methodology can be regarded as stress based finite element analysis as it is required to define the stress distribution within the structural body with structural idealization a...
متن کاملAlgebraic Multigrid Method for Solving 3D Nonlinear Electrostatic and Magnetostatic Field Problems
A recently developed robust Algebraic Multigrid (AMG) method for the efficient solution of 3D nonlinear electrostatic and magnetostatic field problems will be presented. The method is directed to large matrix equations which arise from finite element (FE) discretization where AMG is used as a preconditioner in the Preconditioned Conjugate Gradient (PCG) method. Numerical results will demonstrat...
متن کاملOn Nonoverlapping Domain Decomposition Methods for the Incompressible Navier-stokes Equations
In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version wh...
متن کاملCoupling Nonlinear Element Free Galerkin and Linear Galerkin Finite Volume Solver for 2D Modeling of Local Plasticity in Structural Material
This paper introduces a computational strategy to collaboratively develop the Galerkin Finite Volume Method (GFVM) as one of the most straightforward and efficient explicit numerical methods to solve structural problems encountering material nonlinearity in a small limited area, while the remainder of the domain represents a linear elastic behavior. In this regard, the Element Free Galerkin met...
متن کاملResidual-based a posteriori error estimates for hp finite element solutions of semilinear Neumann boundary optimal control problems
In this paper, we investigate residual-based a posteriori error estimates for the hp finite element approximation of semilinear Neumann boundary elliptic optimal control problems. By using the hp finite element approximation for both the state and the co-state and the hp discontinuous Galerkin finite element approximation for the control, we derive a posteriori error bounds in L2-H1 norms for t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005