Time‐dependent Linearized Infiltration: III. Strip and Disc Sources

Warrick, A. W.; Lomen, D. O.

doi:10.2136/sssaj1976.03615995004000050014x

Cited by 86 publications

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“…The exponential conductivity model was initially proposed by Gardner and later used extensively Warrick and Lomen, 1976). Ignoring spatial variability here, the exponential model is:…”

mentioning

confidence: 99%

Approaches to large scale unsaturated flow in heterogeneous, stratified, and fractured geologic media

Ababou¹

1991

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“…The exponential conductivity model was initially proposed by Gardner and later used extensively Warrick and Lomen, 1976). Ignoring spatial variability here, the exponential model is:…”

mentioning

confidence: 99%

Approaches to large scale unsaturated flow in heterogeneous, stratified, and fractured geologic media

Ababou¹

1991

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“…We consider an exponential model for the permeability tensor a similar to the one in [31], which we slightly modify to simulate an anisotropic porous media, a(s) = e s 0 0 1.1e 1.2s .…”

Section: Numerical Experimentsmentioning

confidence: 99%

A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems

Abdulle

Vilmart

2011

Numer. Math.

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To cite this version:Assyr Abdulle, Gilles Vilmart. A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. Numerische Mathematik, Springer Verlag, 2012, 121, pp.397-431 Abstract The effect of numerical quadrature in finite element methods for solving quasilinear elliptic problems of nonmonotone type is studied. Under similar assumption on the quadrature formula as for linear problems, optimal error estimates in the L 2 and the H 1 norms are proved. The numerical solution obtained from the finite element method with quadrature formula is shown to be unique for a sufficiently fine mesh. The analysis is valid for both simplicial and rectangular finite elements of arbitrary order. Numerical experiments corroborate the theoretical convergence rates.Keywords nonmonotone quasilinear elliptic problem · a priori error estimates · numerical quadrature · variational crime · finite elements.

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“…For the exponential model (see [31] or [15] for more details), we have θ(u) = θ s e βu , K(x,u) = K s (x)e α(x)u . Choosing θ s = 1, β = 0.1.…”

Section: Exponential Model With Periodic Coefficients Consider the Fmentioning

confidence: 99%

Upscaling of a class of nonlinear parabolic equations for the flow transport in heterogeneous porous media

Chen

Deng²,

Huang³

2005

Communications in Mathematical Sciences

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Abstract. We develop an upscaling method for the nonlinear parabolic equationwhich stems from the applications of the flow transport in porous media. Our direct motivation is the Richards equation which models the flow transport in unsaturated porous media. We provide a detailed convergence analysis of the method under the assumption that the oscillating coefficients are periodic. While such a simplifying assumption is not required by our method, it allows us to use homogenization theory to obtain the asymptotic structure of the solutions. Numerical experiments are carried out for the Richards equation of exponential model with periodic and randomly generated log-normal permeability to demonstrate the efficiency and accuracy of the proposed method.

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Time‐dependent Linearized Infiltration: III. Strip and Disc Sources

Cited by 86 publications

References 0 publications

Approaches to large scale unsaturated flow in heterogeneous, stratified, and fractured geologic media

Approaches to large scale unsaturated flow in heterogeneous, stratified, and fractured geologic media

A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems

Upscaling of a class of nonlinear parabolic equations for the flow transport in heterogeneous porous media

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