Divergence-free wavelets play important roles in both partial differential equations and fluid mechanics.Many constructions of those wavelets depend usually on Hermite splines.We study several types of convergence of ...Divergence-free wavelets play important roles in both partial differential equations and fluid mechanics.Many constructions of those wavelets depend usually on Hermite splines.We study several types of convergence of the related Hermite interpolatory operators in this paper.More precisely,the uniform convergence is firstly discussed in the second part;then,the third section provides the convergence in the Donoho's sense.Based on these results,the last two parts are devoted to show the convergence in some Besov spaces,which concludes the completeness of Bittner and Urban's expansions.展开更多
In this paper, we are concerned with uniform superconvergence of Galerkin methods for singularly perturbed reaction-diffusion problems by using two Shishkin-type meshes. Based on an estimate of the error between splin...In this paper, we are concerned with uniform superconvergence of Galerkin methods for singularly perturbed reaction-diffusion problems by using two Shishkin-type meshes. Based on an estimate of the error between spline interpolation of the exact solution and its numerical approximation, an interpolation post-processing technique is applied to the original numerical solution. This results in approximation exhibit superconvergence which is uniform in the weighted energy norm. Numerical examples are presented to demonstrate the effectiveness of the interpolation post-processing technique and to verify the theoretical results obtained in this paper.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10871012)the Natural Science Foundation of Beijing (Grant No.1082003)
文摘Divergence-free wavelets play important roles in both partial differential equations and fluid mechanics.Many constructions of those wavelets depend usually on Hermite splines.We study several types of convergence of the related Hermite interpolatory operators in this paper.More precisely,the uniform convergence is firstly discussed in the second part;then,the third section provides the convergence in the Donoho's sense.Based on these results,the last two parts are devoted to show the convergence in some Besov spaces,which concludes the completeness of Bittner and Urban's expansions.
文摘In this paper, we are concerned with uniform superconvergence of Galerkin methods for singularly perturbed reaction-diffusion problems by using two Shishkin-type meshes. Based on an estimate of the error between spline interpolation of the exact solution and its numerical approximation, an interpolation post-processing technique is applied to the original numerical solution. This results in approximation exhibit superconvergence which is uniform in the weighted energy norm. Numerical examples are presented to demonstrate the effectiveness of the interpolation post-processing technique and to verify the theoretical results obtained in this paper.
