Distributed Lagrange Multiplier Functions for Fictitious Domain Method with Spectral/hp Element Discretization
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A fictitious domain approach for the solution of second-order linear differential problems is proposed; spectral/hp elements have been used for the discretization of the domain. The peculiarity of our approach is that the Lagrange multipliers are particular distributed functions, instead of classical \(\delta \) Dirac (impulsive) multipliers. In this paper we present the formulation and the application of this approach to 1D and 2D Poisson problems and 2D Stokes flow (biharmonic equation).
KeywordsFictitious domain Lagrange multipliers Spectral/hp element method Poisson problem Biharmonic problem
Mathematics Subject Classification65L10 65N35
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