A posteriori error analysis of a cell-centered finite volume method for semilinear elliptic problems
نویسندگان
چکیده
In this paper, we conduct an a posteriori analysis for the error in a quantity of interest computed from a cell-centered finite volume scheme. The a posteriori error analysis is based on variational analysis, residual error and the adjoint problem. To carry out the analysis, we use an equivalence between the cell-centered finite volume scheme and a mixed finite element method with special choice of quadrature.
منابع مشابه
A Posteriori Error Estimate and Adaptive Mesh Refinement for the Cell-Centered Finite Volume Method for Elliptic Boundary Value Problems
We extend a result of Nicaise [13] for the a posteriori error estimation of the cell-centered finite volume method for the numerical solution of elliptic problems. Having computed the piecewise constant finite volume solution uh, we compute a Morley-type interpolant Iuh. For the exact solution u, the energy error ‖∇T (u− Iuh)‖L2 can be controlled efficiently and reliably by a residual-based a p...
متن کاملA Posteriori Error Estimates for Semilinear Boundary Control Problems
In this paper we study the finite element approximation for boundary control problems governed by semilinear elliptic equations. Optimal control problems are very important model in science and engineering numerical simulation. They have various physical backgrounds in many practical applications. Finite element approximation of optimal control problems plays a very important role in the numeri...
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 کاملCell Conservative Flux Recovery and A Posteriori Error Estimate of Vertex-Centered Finite Volume Methods
A cell conservative flux recovery technique is developed here for vertexcentered finite volume methods of second order elliptic equations. It is based on solving a local Neumann problem on each control volume using mixed finite element methods. The recovered flux is used to construct a constant free a posteriori error estimator which is proven to be reliable and efficient. Some numerical tests ...
متن کاملFully Adaptive Newton-Galerkin Methods for Semilinear Elliptic Partial Differential Equations
In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experi...
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:
- J. Computational Applied Mathematics
دوره 233 شماره
صفحات -
تاریخ انتشار 2009