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Author: search.filters.author.Liu, JLSubject: search.filters.subject.a posteriori error estimate

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Now showing 1 - 3 of 3
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    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.
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    Item type:Item,
    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.
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    Item type:Item,
    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.