Some Superconvergence for a Galerkin Method by Averaging Gradients in One Dimensional Problems

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概要

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• We consider some superconvergence phenomena followed by the averaging gradients in a Galerkin method for two point boundary value problems using continuous piecewise polynomials. It is shown that several a posteriori methods based on the averaging procedures yield superconvergent approximations to the exact solution and its derivative with one order better rates of convergence than the optimal rates. The special emphasis of the paper is the fact that the superconvergence phenomena only occur in cases using odd degree polynomials. We illustrate some numerical examples which confirm the theoretical results. Furthermore, we also describe the extension of the results to the parabolic problems in a single space variable.

• 一般社団法人情報処理学会の論文
• 1987-01-31

著者

• Nakao Mitsuhiro

  Kyushu Institute Of Technology

関連論文

• Some Superconvergence for a Galerkin Method by Averaging Gradients in One Dimensional Problems
• Existence of Global Decaying Solutions to the Cauchy Problem for a Nonlinear Dissipative Wave Equation of Klein-Gordon Type with a Derivative Nonlinearity

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