Negative norm error control for second-kind convolution Volterra equations |
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Authors: | Simon Shaw and J.R. Whiteman |
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Affiliation: | (1) BICOM, Brunel University, Uxbridge, UB8 3PH, U.K.; e-mail: {simon.shaw,john.whiteman}@brunel.ac.uk, BICOM: http://www.brunel.ac.uk/~icsrbicm , GB |
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Abstract: | Summary. We consider a piecewise constant finite element approximation to the convolution Volterra equation problem of the second kind: find such that in a time interval . An a posteriori estimate of the error measured in the norm is developed and used to provide a time step selection criterion for an adaptive solution algorithm. Numerical examples are given for problems in which is of a form typical in viscoelasticity theory. Received March 5, 1998 / Revised version received November 30, 1998 / Published online December 6, 1999 |
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Keywords: | Mathematics Subject Classification (1991):3F15 45D05 45K05 65M15 |
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