[PDF] Top 20 New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems

... Recently, optimal control problems have attracted substantial interest due to their appli- cations in atmospheric pollution problems, exploration and extraction of oil and gas re- sources, and ... See full document

... priori error estimates for nonlinear parabolic optimal control problems by mixed finite element ...a posteriori error estimates of triangular ... See full document

... some optimal control problems, for the objective function containing a gradient of the state variable, we use mixed finite element methods to discretize the state equation, so that the ... See full document

... that optimal control problems governed by partial differential equations (PDEs, for short) play a great role in modern science, technology, engineering and so ...finite element approximation of ... See full document

... Optimal control problems appear frequently in the operation of physical, social, economic processes, and other fields, and the numerical solutions of optimal control problems are ... See full document

... mixed finite element methods were used to discrete nonlinear elliptic optimal control problems and derive an L 2 priori error ...priori error ... See full document

... a posteriori error indicator. A posteriori error estimates are computable quan- tities in terms of the discrete solution that measure the actual discrete errors without the knowledge of ... 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, ... See full document

... optimal control problems (see, e.g., [–]). Although bilinear optimal control problems are frequently met in applications, they are much more difficult to handle in comparison to ... See full document

... for nonlinear parabolic integro- differential optimal control ...A posteriori error estimates of finite-element solu- tions for those problems are established ... 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

... such methods. We then review numerical homogenization methods for linear elliptic homogenization problems, nonlinear monotone elliptic homogeniza- tion problems and nonlinear ... See full document

... [r] ... See full document

... In order to improve the quality of the numerical solutions, the continuous interior penalty Galerkin method (CIP Galerkin method) is used to solve the state equation (.). This method was firstly proposed in []. In [, ... See full document

... inhomogeneous and anisotropic diffusion–dispersion tensors). With the techniques from [22], one can also sig- nificantly reduce their computational cost. Considering the finite volume scheme (3.1)–(3.6), it has first of all ... See full document

... In this paper, we derive the finite element error estimates for the approximate solution of mildly nonlinear boundary value problems having auxiliary constraint conditions... ulate it in[r] ... See full document

... global element method in that the sign in front of the so-called symmetric term was ...suboptimal error estimates in the L 2 -norm for numerical solutions can be ... See full document

... finite element methods and then study the space semidis- crete scheme and derive error estimates for the standard Galerkin finite element method with smooth initial ...strong error ... See full document

... the error and the solution of the auxiliary problem (with the residual as right-hand ...a finite dimensional approximation (based on a hierarchical idea) of its ... See full document

... linear finite element approximations of a parabolic ...of finite element schemes for a class of Sobolev equations in R d d ≥ 1, and two order superconvergence results are proved in W ... See full document