We first derive the asymptotic expansion of the bilinear finite volume element for the linear parabolic problem by employing the energy-embedded method on uniform grids, and then obtain a high accuracy combination poi...
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We first derive the asymptotic expansion of the bilinear finite volume element for the linear parabolic problem by employing the energy-embedded method on uniform grids, and then obtain a high accuracy combination pointwise formula of the derivatives for the finite volume element approximation based on the above asymptotic expansion. Furthermore, we prove that the approximate derivatives have the convergence rate of order two. Numerical experiments confirm the theoretical results.
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...
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 sciencecomputation 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 sciencecomputation 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.
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.
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