Browsing by Author "Jou, J"

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A nonconforming weak residual error estimator for elliptic partial differential equations
(1999-09-01)
Jou, J
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
A nonconforming weak residual error estimator is presented and analyzed for finite element solutions of linear elliptic partial differential equations. The treatment of the flux jumps across element edges is of special interest. The estimator is obtained by solving local residual problems which do not explicitly involve the jumps and do not require boundary conditions. The estimator handles both interior and edge residuals on each element by a suitable construction of the basis functions for the local problems. Together with the previous conforming estimator, the weak residual error estimation, without the flux jumps, can thus be applied to both odd- and even-order finite element approximations.
A posteriori boundary element error estimation
(1999-06-15)
Jou, J
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
An a posteriori error estimator is presented for the boundary element method in a general framework. It is obtained by solving local residual problems for which a local concept is introduced to accommodate the fact that integral operators are nonlocal operators. The estimator is shown to have an upper and a lower bound by the constant multiples of the exact error in the energy norm for Symm's and hypersingular integral equations. Numerical results are also given to demonstrate the effectiveness of the estimator for these equations. It can be used for adaptive h, p, and hp methods. (C) 1999 Elsevier Science B.V. All rights reserved.
A posteriori finite element error analysis for symmetric positive differential equations
(1999-01-01)
Jou, J
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
Based on the solution of local weak residual problems, conforming and nonconforming error estimators are presented and analyzed for finite element solutions of symmetric positive differential equations in the sense of Friedrichs. These estimators are devised to treat the Friedrichs system in a general setting in terms of application (hyperbolic as well as mixed-type problems), approximation (h-, p and hp-version finite element methods), implementation (no local boundary conditions and no flux jumps across element boundaries) and a posteriori error analysis (very moderate conditions on the system and on the approximation). Three model problems of the Friedrichs system, namely, the neutron transport equation, the forward-backward heat equation and the Tricomi problem are used to illustrate the applicability of the weak residual error estimation.
A posteriori finite element error analysis for symmetric positive differential equations
(1999-01-01)
Jou, J
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
Based on the solution of local weak residual problems, conforming and nonconforming error estimators are presented and analyzed for finite element solutions of symmetric positive differential equations in the sense of Friedrichs. These estimators are devised to treat the Friedrichs system in a general setting in terms of application (hyperbolic as well as mixed-type problems), approximation (h-, p and hp-version finite element methods), implementation (no local boundary conditions and no flux jumps across element boundaries) and a posteriori error analysis (very moderate conditions on the system and on the approximation). Three model problems of the Friedrichs system, namely, the neutron transport equation, the forward-backward heat equation and the Tricomi problem are used to illustrate the applicability of the weak residual error estimation.
A posteriori least-squares finite element error analysis for the Navier-Stokes equations
(2003-02-01)
Jou, J
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
A residual type a posteriori error estimator is presented for the least-squares finite element solution of stationary incompressible Navier-Stokes equations based on the velocity-vorticity-pressure formulation with nonstandard and standard boundary conditions. Using the coerciveness of the corresponding Stokes operator and the special feature of the nonlineariry of the formulation, it is shown that,the error estimator is exact for the Stokes problem and is asymptotically exact for the Navier-Stokes problem in an energy-like norm. The resulting adaptive method is highly parallel because it does not require to assemble the global, matrix and the error estimation can be completely localized without using any information from neighboring elements.
An a posteriori finite element error analysis for the Stokes equations
(2000-02-01)
Jou, J
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
Conforming and nonconforming error estimators are presented and analyzed for the mixed finite element approximation of the Stokes problem. The estimators are obtained by solving local Poisson-type problems that do not involve boundary conditions, compatibility and balancing conditions, incompressibility constraint, or flux jumps across inter-element boundaries. The estimators are bounded from above and below by constant multiples of the actual error in an energy-like norm and can be used in adaptive h, p, and hp computations. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 65N15; 65N30.
Least-squares finite element approximations to the Timoshenko beam problem
(2000-10-06)
Jou, J
;
Yang, SY
;
應用數學系
;
Department of Applied Mathematics
In this paper a least-squares finite element method for the Timoshenko beam problem is proposed and analyzed. The method is shown to be convergent and stable without requiring extra smoothness of the exact solutions. For sufficiently regular exact solutions, the method achieves optimal order of convergence in the H-1-norm for all the unknowns (displacement, rotation, shear, moment), uniformly in the small parameter which is generally proportional to the ratio of thickness to length. Thus the locking phenomenon disappears as the parameter tends to zero, A sharp a posteriori error estimator which is exact in the energy norm and equivalent in the H-1-norm is also briefly discussed. (C) 2000 Published by Elsevier Science Inc. All rights reserved. AMS classification: 65N15; 65N30.