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Fictitious Domain Approach Via Lagrange Multipliers with Least Squares Spectral Element Method

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Abstract

We consider the application of Fictitious Domain approach combined with Least Squares Spectral Elements for the numerical solution of partial differential equations. Fictitious Domain methods allow problems formulated on a complicated shaped domain Ω to be solved on a simpler domain Π containing Ω. Least Squares Spectral Element Method has been used to develop the discrete model, as this scheme combines the generality of finite element methods with the accuracy of spectral methods. Moreover the least squares methods have theoretical and computational advantages in the algorithmic design and implementation. This paper presents the formulation and validation of the Fictitious Domain/Least Squares Spectral Element approach. The convergence of the relative energy norm η is verified computing smooth solutions to two-dimensional first and second-order differential equations, demonstrating the predictive capability of the proposed formulation.

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  1. Mechanical Engineering Dept., University of Trieste, Via Valerio 10, 34100, Trieste, Italy

    Lucia Parussini

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  1. Lucia Parussini
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Correspondence to Lucia Parussini.

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Parussini, L. Fictitious Domain Approach Via Lagrange Multipliers with Least Squares Spectral Element Method. J Sci Comput 37, 316–335 (2008). https://doi.org/10.1007/s10915-008-9212-x

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  • DOI: https://doi.org/10.1007/s10915-008-9212-x

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