Numerical solution of the eulerian equations of compressible flow by a finite element method which follows the free boundary and the interfaces

Deforming Fluid Domains Within the Finite Element Method: Five Mesh-Based Tracking Methods in Comparison

“…The space-time method offers the unique opportunity to write the variational form directly over a deforming domain. This concept was pioneered by Jamet and Bonnerot [121,31,77,148,120]. It was later extended concurrently by Tezduyar et al [207] in the form of the Deformable-Spatial-Domain/Stabilized Space-Time (DSD/SST) method, also applied in [23,160], and by Hansbo [100] with a particular mesh moving scheme conforming to the characteristic streamline diffusion ideology.…”

An Adaptive Finite Element Method for Initial-Boundary Value Problems for Partial Differential Equations

“…To do this we develop methods that (i) discretize We discretize (1.1)-(1.3) using a finite element Galerkin method on trapezoidal space-time elements. This approach is similar to that of Jamet and Bonnerot [6,22] and it was chosen because it is generally easier to generate high order approximations to partial differential equations on a nonuniform mesh with finite element methods than with finite difference methods. The accuracy and order of convergence of our methods are analyzed in Davis [11] and are demonstrated experimentally in Section 4 of this paper.…”

Improvement of MacCormack's scheme for Burgers' equation. Using a finite element method

“…., N) of the domain of computation. Since u = u or u = u2 (both cases are analysed), the conditions of integrability of equations ( 5 ) and (6) require that the function u be at least piecewise constant. This choice leads to the method of M a~C o r m a c k .~…”