Optimal control of soil venting: mathematical modeling and applications

Gierke, John S.

doi:10.1016/s0005-1098(01)00017-6

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K(t S)v(s)ds1

Full Discretization1

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2015

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“…For more information, we refer the reader to [2,3]. More applications of the BCs in (1) can be found in [4,5].…”

Section: K(t S)v(s)dsmentioning

confidence: 99%

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Full discretization of a nonlinear parabolic problem containing volterra operators and an unknown dirichlet boundary condition

Grimmonprez

Slodička

2015

Numer. Methods Partial Differential Eq.

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The reconstruction of an unknown solely time-dependent Dirichlet boundary condition in a nonlinear parabolic problem containing a linear and a nonlinear Volterra operator is considered. The inverse problem is converted into a variational problem in which the unknown Dirichlet condition is eliminated using a given integral overdetermination. A time-discrete recurrent approximation scheme is designed, using Backward Euler's method. The convergence of the approximations towards a solution of the variational problem is proved under appropriate assumptions on the data and on the Volterra operators. The uniqueness of this solution is shown in the case that the nonlinear Volterra operator satisfies a particular inequality. Moreover, the Finite Element Method is used to discretize the time-discrete approximation scheme in space. Finally, full-discrete error estimates are derived for a particular choice of the finite elements. The corresponding convergence rates are supported by a numerical experiment.

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“…For more information, we refer the reader to [2,3]. More applications of the BCs in (1) can be found in [4,5].…”

Section: K(t S)v(s)dsmentioning

confidence: 99%

“…Moreover, assume that (2), (4), and (5) are satisfied. Then there exist positive constants C and τ 0 such that, ∀τ ≤ τ 0 ,…”

Section: Full Discretizationmentioning

confidence: 99%

Full discretization of a nonlinear parabolic problem containing volterra operators and an unknown dirichlet boundary condition

Grimmonprez

Slodička

2015

Numer. Methods Partial Differential Eq.

View full text Add to dashboard Cite

show abstract

Optimal control of soil venting: mathematical modeling and applications

Cited by 1 publication

References 2 publications

Full discretization of a nonlinear parabolic problem containing volterra operators and an unknown dirichlet boundary condition

Full discretization of a nonlinear parabolic problem containing volterra operators and an unknown dirichlet boundary condition

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