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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Resolvent estimates for elliptic finite element operators in one dimension
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by M. Crouzeix, S. Larsson and V. Thomée PDF
Math. Comp. 63 (1994), 121-140 Request permission

Abstract:

We prove the analyticity (uniform in h) of the semigroups generated on ${L_p}(0,1),1 \leq p \leq \infty$, by finite element analogues ${A_h}$ of a one-dimensional second-order elliptic operator A under Dirichlet boundary conditions. This is accomplished by showing the appropriate estimates for the resolvents by means of energy arguments. The results are applied to prove stability and optimal-order error bounds for numerical solutions of the associated parabolic problem for both smooth and nonsmooth data.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 63 (1994), 121-140
  • MSC: Primary 65N30; Secondary 65M60
  • DOI: https://doi.org/10.1090/S0025-5718-1994-1242058-1
  • MathSciNet review: 1242058