Interpolation error-based a posteriori error estimation for two-point boundary value problems and parabolic equations in one space dimension |
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Authors: | Peter K Moore |
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Institution: | (1) Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA; e-mail: pmoore@mail.smu.edu , US |
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Abstract: | Summary. I derive a posteriori error estimates for two-point boundary value problems and parabolic equations in one dimension based on interpolation error
estimates. The interpolation error estimates are obtained from an extension of the error formula for the Lagrange interpolating
polynomial in the case of symmetrically-spaced interpolation points. From this formula pointwise and seminorm a priori estimates of the interpolation error are derived. The interpolant in conjunction with the a priori estimates is used to obtain asymptotically exact a posteriori error estimates of the interpolation error. These a posteriori error estimates are extended to linear two-point boundary problems and parabolic equations. Computational results demonstrate
the convergence of a posteriori error estimates and their effectiveness when combined with an hp-adaptive code for solving parabolic systems.
Received April 17, 2000 / Revised version received September 25, 2000 / Published online May 30, 2001 |
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Keywords: | Mathematics Subject Classification (1991): 65M15 65M20 65M60 |
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