In this paper,the time-dependent Maxwell’s equations used to modeling wave propagation in dispersive lossy bi-isotropic media are *** and uniqueness of the modeling equations are *** fully discrete finite element sch...
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In this paper,the time-dependent Maxwell’s equations used to modeling wave propagation in dispersive lossy bi-isotropic media are *** and uniqueness of the modeling equations are *** fully discrete finite element schemes are proposed,and their practical implementation and stability are discussed.
In this paper, combining some special eigenvalue inequalities of matrix’s product and sum with the equivalent form of the continuous coupled algebraic Riccati equation (CCARE), we construct linear inequalities. Then,...
In this paper, combining some special eigenvalue inequalities of matrix’s product and sum with the equivalent form of the continuous coupled algebraic Riccati equation (CCARE), we construct linear inequalities. Then, in terms of the properties of M-matrix and its inverse matrix, through solving the derived linear inequalities, we offer new upper matrix bounds for the solution of the CCARE, which improve some of the recent results. Finally, we present a corresponding numerical example to show the effectiveness of the given results.
Two-level additive preconditioners are presented for edge element discretizations of time-harmonic Maxwell equations. The key is to construct a special “coarse mesh” space, which adds the kernel of the curl -operato...
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Two-level additive preconditioners are presented for edge element discretizations of time-harmonic Maxwell equations. The key is to construct a special “coarse mesh” space, which adds the kernel of the curl -operator in a fine space to a coarse mesh space, to solve the original problem, and then uses the fine mesh space to solve the H ( curl ) -elliptic problem. It is shown that the generalized minimal residual (GMRES) method applied to the preconditioned system converges uniformly provided that the coarsest mesh size is reasonably small (but independent of the fine mesh size) and the parameter for the “coarse mesh” space solver is sufficiently large. Numerical experiments show the efficiency of the proposed approach.
We discuss the cubic spline collocation method with two parameters for solving the initial value problems (IVPs) of fractional differential equations (FDEs). Some results of the local truncation error, the convergence...
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In this paper,a new numerical algorithm for solving the time fractional Fokker-Planck equation is *** analysis of local truncation error and the stability of this method are *** analysis and numerical experiments show...
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In this paper,a new numerical algorithm for solving the time fractional Fokker-Planck equation is *** analysis of local truncation error and the stability of this method are *** analysis and numerical experiments show that the proposed method has higher order of accuracy for solving the time fractional Fokker-Planck equation.
We propose some new weighted averaging methods for gradient recovery,and present analytical and numerical investigation on the performance of these weighted averaging *** is shown analytically that the harmonic averag...
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We propose some new weighted averaging methods for gradient recovery,and present analytical and numerical investigation on the performance of these weighted averaging *** is shown analytically that the harmonic averaging yields a superconvergent gradient for any mesh in one-dimension and the rectangular mesh in *** results indicate that these new weighted averaging methods are better recovered gradient approaches than the simple averaging and geometry averaging methods under triangular mesh.
High quality mesh plays an important role for finite element methods in science computation and numerical *** the mesh quality is good or not,to some extent,it determines the calculation results of the accuracy and **...
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High quality mesh plays an important role for finite element methods in science computation and numerical *** the mesh quality is good or not,to some extent,it determines the calculation results of the accuracy and *** from classic Lloyd iteration algorithm which is convergent slowly,a novel accelerated scheme was presented,which consists of two core parts:mesh points replacement and local edges Delaunay *** using it,almost all the equilateral triangular meshes can be generated based on centroidal Voronoi tessellation(CVT).Numerical tests show that it is significantly effective with time consuming decreasing by 40%.Compared with other two types of regular mesh generation methods,CVT mesh demonstrates that higher geometric average quality increases over 0.99.
In this paper,we develop a correction operator for the canonical interpolation operator of the Adini *** use this new correction operator to analyze the discrete eigenvalues of the Adini element method for the fourth ...
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In this paper,we develop a correction operator for the canonical interpolation operator of the Adini *** use this new correction operator to analyze the discrete eigenvalues of the Adini element method for the fourth order elliptic eigenvalue problem in the three *** prove that the discrete eigenvalues are smaller than the exact ones.
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.
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