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Quasi-Optimal Convergence Rate of an Adaptive Weakly Over-Penalized Interior Penalty Method

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Abstract

We analyze an adaptive discontinuous finite element method (ADFEM) for the weakly over-penalized symmetric interior penalty (WOPSIP) operator applied to symmetric positive definite second order elliptic boundary value problems. For first degree polynomials, we prove that the ADFEM is a contraction for the sum of the energy error and the scaled error estimator between two consecutive loops of the adaptive algorithm. After establishing this geometric decay, we define a suitable approximation class and prove that the adaptive WOPSIP method obeys a quasi-optimal rate of convergence.

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  1. Automated Trading Desk, 11 eWall Street, Mount Pleasant, SC, 29464, USA

    Luke Owens

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  1. Luke Owens
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Correspondence to Luke Owens.

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The work of this author was partially supported by Dod-Navy-Office Of Naval Research under Award Number N000140811113.

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Owens, L. Quasi-Optimal Convergence Rate of an Adaptive Weakly Over-Penalized Interior Penalty Method. J Sci Comput 59, 309–333 (2014). https://doi.org/10.1007/s10915-013-9765-1

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