Modeling arteriolar flow and mass transport using the immersed boundary method
Journal of Computational Physics
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow
Journal of Computational Physics
Journal of Computational Physics
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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 驴 to be solved on a simpler domain 驴 containing 驴. 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 驴 is verified computing smooth solutions to two-dimensional first and second-order differential equations, demonstrating the predictive capability of the proposed formulation.