Discontinuous Galerkin method with a posterioriL_p(0,t_i)
error estimate for second-kind Volterra problems |
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Authors: | S Shaw JR Whiteman |
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Institution: | (1) Brunel University, Uxbridge, Middlesex UB8 3PH, England , GB |
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Abstract: | Summary.
We consider a discontinuous Galerkin finite element method
applied in time to a model Volterra equation of the second kind.
A residual-based computable
Galerkin-error estimate is derived
for .
This estimate does not explicitly
contain the time step and therefore the time step
control must be based
on a heuristic criterion, the estimate can then be used to
demonstrate the integrity, or otherwise, of the finite element
solution. After performing some numerical experiments
we conclude that this approach is at least competetive
with classical discretizations since it is
computationally simple to implement,
but has the added advantage of
reliable error feedback.
Received June 25, 1995 |
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Keywords: | Mathematics Subject Classification (1991): 45D05 65M15 65M60 73F15 |
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