[PDF] Top 20 A posteriori error estimates for fourth order hyperbolic control problems by mixed finite element methods

... finite element approximation for optimal control problems has an enormously im- portant function in the numerical approach for these ...ror estimates using finite element approximations, ... See full document

... the mixed finite element methods for general convex optimal control problems governed by integro-differential ...lowest order Raviart-Thomas mixed finite element ... See full document

... the order one Raviart- Thomas mixed finite element to discretize the state and the ...optimal control u in general, we therefore only consider a piecewise con- stant ...a posteriori ... See full document

... In this section, we shall study the mixed finite element and the backward Euler discretiza- tion approximation of convective diffusion optimal control problems (.)-(.). For the sake of ... See full document

... many control problems, the objective functional contains gradient of the state ...the finite element community, mixed finite element methods should be used for ... See full document

... The mixed finite element methods (MFEM) are widely used in the theoretical analysis and computations of many areas of science and ...convergence order, it becomes more and more popular ... See full document

... optimal control problems are very important for modeling in ...optimal control prob- lems plays a very important role in the numerical methods for these ...finite- element approximation ... See full document

... Optimal control problems have attracted substantial interest in recent years due to their applications in aero-hydrodynamics, atmospheric, hydraulic pollution problems, combus- tion, exploration and ... See full document

... finite element methods for quadratic boundary optimal control problems governed by nonlinear parabolic ...a posteriori error estimates for the state and control ... See full document

... diffusion methods (Asadzadeh [6]; Asadza- deh and Kowalczyk [7]; Eriksson and Johnson [8]; Brenner [9]; Dubois [10]; Fuhrer [11] ) perform slightly better than the standard finite element ... See full document

... A posteriori estimation is a key tool for the control of the discretization error aris- ing in numerical simulations involving the finite element method [1, 3, ...a posteriori ... See full document

... a posteriori error estimation in the finite volume and lowest-order Raviart–Thomas mixed finite element ...Our estimates are derived in the energy (semi-)norm for a locally ... See full document

... the mixed finite element method to deal with fourth order hyperbolic optimal control ...a posteriori error estimates and superconvergence of mixed ... See full document

... a posteriori error estimates for the hp version of the finite element approximation of nonlinear parabolic optimal control ...finite element approximation for both the state and ... See full document

... [11] G. Adomian and R. Rach, “Analytic Solution of Nonlin- ear Boundary-Value Problems in Several Dimensions by Decomposition,” Journal of Mathematical Analysis and Applications, Vol. 174, No. 1, 15 March 1993, ... See full document

... variable. The operator A : D(A) ⊂ H → H is not necessarily a bounded, linear, densely defined, and selfadjoint operator with compact inverse. The nonlinear operators f and g are Lipschitz continuous in an appropriate ... See full document

... In this section, we verify the theoretical findings in previous sections by the following three numerical examples: the first one is for a problem with a known smooth solution, the second one is for a problem on L-shape ... See full document

... the error between the analytical and numerical solutions, the "majority rule" approach imposes a weighting system on a system of six variables with varying degrees of ... See full document

... finite element method for solving bilinear parabolic optimal control problems is ...finite element approximation of the model ...their error estimates. Thirdly, we derive a priori ... See full document

... a posteriori error estimates in the finite element method discretization of the Poisson equation, introduced in ...A posteriori error estimation in the conforming ... See full document