Finite Element Approximation of a Rigid Punch Indenting a Membrane |
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Authors: | BARRETT JOHN W; CHAKRABARTI ROMA; ELLIOTT CHARLES M |
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Institution: |
Department of Mathematics, Imperial College London SW7 2BZ
Department of Mathematics, Brighton Polytechnic Brighton, Sussex BN2 4GJ
School of Mathematical and Physical Sciences, University of Sussex Brighton, Sussex BN1 9QH
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Abstract: | Optimal order H1 and L error bounds are obtained for a continuouspiecewise linear finite element approximation of an obstacleproblem, where the obstacle's height as well as the contactzone, c, are a priori unknown. The problem models the indentationof a membrane by a rigid punch. For R2, given ,g R+ and an obstacle defined over E we consider the minimization of |v|21,+gµover (v, µ) H10() x R subject to v+µ on E. In additionwe show under certain nondegeneracy conditions that dist (c,hc)Ch ln 1/h, where hc is the finite element approximation toc. Finally we show that the resulting algebraic problem canbe solved using a projected SOR algorithm. |
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