A finite element method to compute elastoacoustic vibration modes in 3D problems on hexahedral meshes is analyzed. It is based on displacement formulations for fluid and solid. In order to avoid spurious modes, the discretization consists of lowest-order hexahedral Raviart-Thomas elements for the former coupled with classical trilinear isoparametric hexahedral elements for the latter. The kinem...

The development of higher order finite elements methods has become an active research area [1]. The deformation method for mesh generation has achieved a prescribed positive Jacobian determinant constraint [2] [3] and it has been a useful method for mesh adaptation [4] [5] [6]. In this work, the deformation method is combined with local refinement to generate higher order meshes. 2D and 3D nume...

BACKGROUND Finite element method (FEM) analysis for intraoperative modeling of the left ventricle (LV) is presently not possible. Since 3D structural data of the LV is now obtainable using standard transesophageal echocardiography (TEE) devices intraoperatively, the present study describes a method to transfer this data into a commercially available FEM analysis system: ABAQUS. METHODS In thi...

For a plane polygonal domain Q and a corresponding (general) triangulation we define classes of functions pmix, v) which are polynomials on each triangle and which are in C^'CQ) and also belong to the Sobolev space ^""^'(n). Approximation theoretic properties are proved concerning these functions. These results are then applied to the approximate solution of arbitrary-order elliptic boundary va...

This work shows that the method of charcteristics is well suited for the numerical solution of first order hyperbolic partial differential equations whose coefficients are approximated by functions piecewise constant on a finite element triangulation of the domain of integration. We apply this method to the numerical solution of Euler's equation and prove convergence when the time step and the ...