Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Computer Methods in Applied Mechanics and Engineering
On some techniques for approximating boundary conditions in the finite element method
Modelling 94 Proceedings of the 1994 international symposium on Mathematical modelling and computational methods
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Finite Element Methods of Least-Squares Type
SIAM Review
Modeling arteriolar flow and mass transport using the immersed boundary method
Journal of Computational Physics
An adaptive version of the immersed boundary method
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
A Fat Boundary Method for the Poisson Problem in a Domain with Holes
Journal of Scientific Computing
A Least-Squares Spectral Element Formulation for the Stokes Problem
Journal of Scientific Computing
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Spectral distributed Lagrange multiplier method: algorithm and benchmark tests
Journal of Computational Physics
A DLM/FD method for fluid/flexible-body interactions
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
A fictitious domain approach to the numerical solution of PDEs in stochastic domains
Numerische Mathematik
Fictitious Domain Approach Via Lagrange Multipliers with Least Squares Spectral Element Method
Journal of Scientific Computing
A second order virtual node method for elliptic problems with interfaces and irregular domains
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions
Journal of Computational Physics
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method
Computational Mechanics
Hi-index | 31.47 |
We consider the application of Fictitious Domain approach combined with least squares spectral elements for the numerical solution of fluid dynamic incompressible equations. Fictitious Domain methods allow problems formulated on a complicated shaped domain @W to be solved on a simpler domain @P containing @W. 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 for the steady incompressible Navier-Stokes equations. The convergence of the approximated solution is verified solving two-dimensional benchmark problems, demonstrating the predictive capability of the proposed formulation.