<span style="font-family:Verdana;">Beam equation can describe the deformation of beams and reflect various bending problems and it has been widely used in large engineering projects, bridge constructio...<span style="font-family:Verdana;">Beam equation can describe the deformation of beams and reflect various bending problems and it has been widely used in large engineering projects, bridge construction, aerospace and other fields. It has important engineering practice value and scientific significance for the design of numerical schemes. In this paper, a scheme for vibration equation of viscoelastic beam is developed by using the Hermite finite element. Based on an elliptic projection, the errors of semi-discrete scheme and fully discrete scheme are analyzed respectively, and the optimal </span><i><span style="font-family:Verdana;">L</span></i><sup><span style="font-family:Verdana;vertical-align:super;">2</span></sup><span style="font-family:Verdana;">-norm error estimates are obtained. Finally, a numerical example is given to verify the theoretical predictions and the validity of the scheme.展开更多
A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and con- tinuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of ...A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and con- tinuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of C2 continuity are proved. Geometric features of subdivision curves, such as line segments, cusps and inflection points, are obtained by appending some conditions to initial vectorial Hermite sequence. An algorithm is presented for generating geometric features. For an initial se- quence of two-order Hermite elements from unit circle, the numerical error of the 4th subdivided level is O(10?4).展开更多
In this paper, we present a finite volume framework for second order elliptic equations with variable coefficients based on cubic Hermite element. We prove the optimal H1 norm error estimates. A numerical example is g...In this paper, we present a finite volume framework for second order elliptic equations with variable coefficients based on cubic Hermite element. We prove the optimal H1 norm error estimates. A numerical example is given at the end to show the feasibility of the method.展开更多
Provides information on a study which discussed the convergence and superconvergence for eigenvalue problem of the biharmonic equation using the Hermite bicubic element. Discussion on eigenvalue problem for biharmonic...Provides information on a study which discussed the convergence and superconvergence for eigenvalue problem of the biharmonic equation using the Hermite bicubic element. Discussion on eigenvalue problem for biharmonic equation; Background on asymptotic error expansions and interpolation postprocessing; Superconvergence approximations to the eigenvalue and eigenfunction.展开更多
文摘<span style="font-family:Verdana;">Beam equation can describe the deformation of beams and reflect various bending problems and it has been widely used in large engineering projects, bridge construction, aerospace and other fields. It has important engineering practice value and scientific significance for the design of numerical schemes. In this paper, a scheme for vibration equation of viscoelastic beam is developed by using the Hermite finite element. Based on an elliptic projection, the errors of semi-discrete scheme and fully discrete scheme are analyzed respectively, and the optimal </span><i><span style="font-family:Verdana;">L</span></i><sup><span style="font-family:Verdana;vertical-align:super;">2</span></sup><span style="font-family:Verdana;">-norm error estimates are obtained. Finally, a numerical example is given to verify the theoretical predictions and the validity of the scheme.
文摘A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and con- tinuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of C2 continuity are proved. Geometric features of subdivision curves, such as line segments, cusps and inflection points, are obtained by appending some conditions to initial vectorial Hermite sequence. An algorithm is presented for generating geometric features. For an initial se- quence of two-order Hermite elements from unit circle, the numerical error of the 4th subdivided level is O(10?4).
基金The Major State Basic Research (1999032803) of China, the NNSF (10372052, 10271066)of China and the Doctorate Foundation (20030422047) of the Ministry of Education of China.
文摘In this paper, we present a finite volume framework for second order elliptic equations with variable coefficients based on cubic Hermite element. We prove the optimal H1 norm error estimates. A numerical example is given at the end to show the feasibility of the method.
文摘Provides information on a study which discussed the convergence and superconvergence for eigenvalue problem of the biharmonic equation using the Hermite bicubic element. Discussion on eigenvalue problem for biharmonic equation; Background on asymptotic error expansions and interpolation postprocessing; Superconvergence approximations to the eigenvalue and eigenfunction.
