QA239 : Adaptive Finite Element Methods For Elliptic Problems With Discontinuous Coefficients
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2014
Authors:
Abstarct: Elliptic partial diferential equations (PDEs) with discontinuous difusion coeficients
occur in application domains such as difusions through porous media, electromagnetic field propagation on heterogeneous media, and difusion processes on
rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could
even be unknown beforehand. One of the obstacles to treating such discontinuity
problems is that the usual perturbation theory for elliptic PDEs assumes bounds
for the distortion of the coeficients in the L1 norm and this in turn requires that
the discontinuities are matched exactly when the coeficients are approximated. We
present a new approach baxsed on distortion of the coeficients in an Lq norm with
q < 1 which therefore does not require the exact matching of the discontinuities.
We then use this new distortion theory to formulate new adaptive finite element
methods (AFEMs) for such discontinuity problems. We show that such AFEMs
are optimal in the sense of distortion versus number of computations, and report
insightful numerical results supporting our analysis.
Keywords:
#Elliptic Problem #Discontinuous Coeffcients #Perturbation Estimates #Adaptive Finite Element Methods #Optimal Rates of Convergence Link
Keeping place: Central Library of Shahrood University
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Keeping place: Central Library of Shahrood University
Visitor: