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A smooth fictitious domain/multiresolution method for elliptic equations on general domains

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Abstract

We propose a smooth fictitious domain/multiresolution method for enhancing the accuracy order in solving second order elliptic partial differential equations on general bivariate domains. We prove the existence and uniqueness of the solution of a corresponding discrete problem and a so-called interior error estimate which justifies the improved accuracy order. Numerical experiments are conducted on a Cassini oval.

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Correspondence to Ping Yin.

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Yin, P., Liandrat, J. A smooth fictitious domain/multiresolution method for elliptic equations on general domains. Numer Algor 72, 705–720 (2016). https://doi.org/10.1007/s11075-015-0063-x

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  • DOI: https://doi.org/10.1007/s11075-015-0063-x

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