We will present a set of equations for General Relativity adapted to weak simplicial spacetimes. The equations will be obtained via a weak formulation of the field equations similar to the methods commonly used in finite element schemes. The equations will be shown to be a weighted sum of the Regge equations.

Semidiscrete finite element approximations of a linear fluid-structure interaction problem are studied. First, results concerning a divergence-free weak formulation of the interaction problem are reviewed. Next, semidiscrete finite element approximations are defined, and the existence of finite element solutions is proved with the help of an auxiliary, discretely divergence-free formulation. A ...

Recently Masud and Hughes proposed a stabilized mixed finite element formulation for Darcy flow. An interesting feature of this formulation is that there are no mesh-dependent parameters. In the present work we provide a derivation of this formulation based on a multiscale decomposition of the solution. We also extend the work of Masud and Hughes to three-dimensional problems and show the conve...

The occurrence of spurious solutions is a well-known limitation of the standard nodal finite element method when applied to electromagnetic problems. The two commonly used remedies that are used to address this problem are (i) The addition of a penalty term with the penalty factor based on the local dielectric constant, and which reduces to a Helmholtz form on homogeneous domains (regularized f...

We consider the tensorial diffusion equation, and address the discrete maximumminimum principle of mixed finite element formulations. In particular, we address non-negative solutions (which is a special case of the maximum-minimum principle) of mixed finite element formulations. It is well-known that the classical finite element formulations (like the single-field Galerkin formulation, and Ravi...

The paper gives an introduction to rate equations in nonlinear continuum mechanics which should obey specific transformation rules. Emphasis is placed on the geometrical nature of the operations involved in order to clarify the different concepts. The paper is particularly concerned with common classes of constitutive equations based on corotational stress rates and their proper implementation ...