Error estimates of finite volume method for Stokes optimal control problem

The Optimal L2 Error Estimate of Stabilized Finite Volume Method for the Stationary Navier-Stokes Problem

Equivalent a posteriori error estimates for spectral element solutions of constrained optimal control problem in one dimension

‎In this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎The equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎Such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.

Some Error Estimates for the Finite Volume Element Method for a Parabolic Problem

We study spatially semidiscrete and fully discrete finite volume element methods for the homogeneous heat equation with homogeneous Dirichlet boundary conditions and derive error estimates for smooth and nonsmooth initial data. We show that the results of our earlier work [Math. Comp. 81 (2012), 1–20] for the lumped mass method carry over to the present situation. In particular, in order for er...

An Optimal Adaptive Finite Element Method for the Stokes Problem

A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur complement system that arises by eliminating the velocity. Each of the arising finite element problems...

Finite Volume Scheme for Stokes Problem

For Stokes problem, we show how to obtain nite volume schemes from a Mixed nite element method with a well chosen numerical integration diagonalising the mass matrix. The analysis of the corresponding nite volume scheme is directly deduced from general results of mixed nite element theory. In this note, we exhibit nite volume scheme for Stokes problem and give optimal a priori error estimate. R...