We study the two dimensional time dependent Large Eddy Simulation method applied to incompressible Navier–Stokes system with Smagorinsky’s eddy viscosity model and a filter width that depends on local mesh size. The discrete is based implicit Euler scheme conforming finite element for space discretizations, respectively. establish reliable efficient posteriori error estimation between numerical...

A posteriori error estimates are constructed for the three-field variational formulation of Biot problem involving displacements, total pressure and fluid pressure. The discretization under focus is H1(?)-conforming Taylor–Hood finite element combination, consisting polynomial degrees k+1 displacements k An a estimator derived on basis H(div)-conforming reconstructions stress flux approximation...

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...

We consider discretizations of convection dominated nonstationary convectiondiffusion equations by A-stable θ-schemes in time and conforming finite elements in space on locally refined, isotropic meshes. For these discretizations we derive a residual a posteriori error estimator. The estimator yields upper bounds on the error which are global in space and time and lower bounds that are global i...

An implicit a posteriori error estimation technique is presented and analyzed for the numerical solution of the time-harmonic Maxwell equations using Nédélec edge elements. For this purpose we define a weak formulation for the error on each element and provide an efficient and accurate numerical solution technique to solve the error equations locally. We investigate the well-posedness of the er...

We prove pointwise a posteriori error estimates for semiand fullydiscrete finite element methods for approximating the solution u to a parabolic model problem. Our estimates may be used to bound the finite element error ‖u−uh‖L∞(D), where D is an arbitrary subset of the space-time domain of definition of the given PDE. In contrast to standard global error estimates, these estimators de-emphasiz...