This paper is concerned with recovery type a posteriori error estimates of fully discrete finite element approximation for general convex parabolic optimal control problems with pointwise control *** time discretizati...
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This paper is concerned with recovery type a posteriori error estimates of fully discrete finite element approximation for general convex parabolic optimal control problems with pointwise control *** time discretization is based on the backward Euler *** state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant *** derive the superconvergence properties of finite element *** using the superconvergence results,we obtain recovery type a posteriori error *** numerical examples are presented to verify the theoretical results.
In this paper,we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic *** state and the co-state are discretized by the high o...
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In this paper,we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic *** state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant *** derive a posteriori error estimates for both the state and the control *** estimates,which are apparently not available in the literature,are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.
In this paper, we propose two parallel Hilbert Space-filling Curve(HSFC) generation algorithms BMIMp and SDDMp based on block matrix iteration method(BMIM) and state diagrams driver method(SDDM) in the CUDA parallel p...
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In this paper,we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control *** state and co-state are approximated by the lowest order Raviart-Thomas mi...
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In this paper,we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control *** state and co-state are approximated by the lowest order Raviart-Thomas mixed fi-nite element spaces and the control variable is approximated by piecewise constant *** derive L^(2) and L^(∞)-error estimates for the control ***,using a recovery operator,we also derive some superconvergence results for the control ***,a numerical example is given to demonstrate the theoretical results.
In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral *** state and co-state are approximated...
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In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral *** state and co-state are approximated by the order one Raviart-Thomas mixed finite element space and the control variable is approximated by piecewise constant functions or piecewise linear *** derive some superconvergence results for the control variable and the state variables when the control is approximated by piecewise constant ***,we derive L∞-error estimates for both the control variable and the state variables when the control is discretized by piecewise linear ***,some numerical examples are given to demonstrate the theoretical results.
We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without res...
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We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale *** key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary *** boundary conditions are chosen to extract more accurate boundary information in the local *** consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base *** examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.
In this paper,we propose a variational multiscale method(VMM)for the stationary incompressible magnetohydrodynamics *** method is defined by large-scale spaces for the velocity field and the magnetic field,which aims ...
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In this paper,we propose a variational multiscale method(VMM)for the stationary incompressible magnetohydrodynamics *** method is defined by large-scale spaces for the velocity field and the magnetic field,which aims to solve flows at high Reynolds *** provide a new VMM formulation and prove its stability and ***,some numerical experiments are presented to indicate the optimal convergence of our method.
In this paper,we propose an iterative two-grid method for the edge finite element discretizations(a saddle-point system)of Perfectly Matched Layer(PML)equations to the Maxwell scattering problem in two ***,we use a fi...
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In this paper,we propose an iterative two-grid method for the edge finite element discretizations(a saddle-point system)of Perfectly Matched Layer(PML)equations to the Maxwell scattering problem in two ***,we use a fine space to solve a discrete saddle-point system of H(grad)variational problems,denoted by auxiliary system ***,we use a coarse space to solve the original saddle-point ***,we use a fine space again to solve a discrete H(curl)-elliptic variational problems,denoted by auxiliary system ***,we develop a regularization diagonal block preconditioner for auxiliary system 1 and use H-X preconditioner for auxiliary system *** we essentially transform the original problem in a fine space to a corresponding(but much smaller)problem on a coarse space,due to the fact that the above two preconditioners are efficient and *** with some existing iterative methods for solving saddle-point systems,such as PMinres,numerical experiments show the competitive performance of our iterative two-grid method.
In this work,we investigate wave propagation through a zero index meta-material(ZIM)waveguide embedded with triangular dielectric *** provide a theoretical guidance on how to achieve total reflection and total transmis...
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In this work,we investigate wave propagation through a zero index meta-material(ZIM)waveguide embedded with triangular dielectric *** provide a theoretical guidance on how to achieve total reflection and total transmission(i.e.,cloaking)by adjusting the defect sizes and/or permittivities of the *** work provides a systematical way in manipulating wave propagation through ZIM in addi-tion to the widely studied dielectric defects with cylindrical and rectangular geome-tries.
In this paper, a linearly implicit conservative difference scheme for the coupled nonlinear Schrödinger equations with space fractional derivative is proposed. This scheme conserves the mass and energy in the dis...
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