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Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains

100%

Borsuk M.

Annales Polonici Mathematici

1998

tom 69

nr 2

129-154

We consider generalized solutions to the Dirichlet problem for linear elliptic second order equations in a domain bounded by a Dini-Lyapunov surface and containing a conical point. For such solutions we derive Dini estimates for the first order generalized derivatives.

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Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems

100%

Kahlbacher M., Volkwein S.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2007

tom 27

nr 1

95-117

Proper orthogonal decomposition (POD) is a powerful technique for model reduction of linear and non-linear systems. It is based on a Galerkin type discretization with basis elements created from the system itself. In this work, error estimates for Galerkin POD methods for linear elliptic, parameter-dependent systems are proved. The resulting error bounds depend on the number of POD basis functions and on the parameter grid that is used to generate the snapshots and to compute the POD basis. The error estimates also hold for semi-linear elliptic problems with monotone nonlinearity. Numerical examples are included.

Error estimates for finite element approximations of elliptic control problems

100%

Alt W., Bräutigam N., Rösch A.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2007

tom 27

nr 1

7-22

We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.

Ograniczanie wyników

2 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Annales Polonici Mathematici

1 Alt W.

1 Borsuk M.

1 Bräutigam N.

1 Kahlbacher M.

1 Rösch A.

1 Volkwein S.

2 2007

1 1998

Wyniki wyszukiwania

Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains

Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems

Error estimates for finite element approximations of elliptic control problems