Abstract
Consider a homogeneous parabolic problem on a smooth bounded domain in ℝN but with initial data and Neumann boundary data of low regularity. Sharp interior maximum norm error estimates are given for a semidiscrete C 0 finite element approximation to this problem. These estimates are obtained by first establishing a new localized L ∞ estimate for semidiscrete finite element approximations on interior subdomains. Numerical examples illustrate the findings.
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AMS subject classification (2000)
65N30
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Solo, A. Sharp estimates for finite element approximations to parabolic problems with Neumann boundary data of low regularity . Bit Numer Math 48, 117–137 (2008). https://doi.org/10.1007/s10543-007-0157-5
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DOI: https://doi.org/10.1007/s10543-007-0157-5