This paper introduces the basic concepts for physics-compatible discretization techniques.
The paper gives a clear distinction between vectors and forms. Based on the difference …

In this paper higher order mimetic discretizations are introduced which are firmly rooted in
the geometry in which the variables are defined. The paper shows how basic constructs in …

We introduce a new finite element (FE) discretization framework applicable for covariant split
equations. The introduction of additional differential forms (DF) that form pairs with the …

We introduce locally conservative, structure-preserving split finite element (FE)
discretizations of a y-independent (slice) model of the covariant rotating shallow water …

Physical systems in the continuous domain are often solved using computer-aided software
because of their complexity. Preserving the physical quantities from the continuous domain …

Numerical Solution of Advection Equation with the Discretization of the Lie Derivative Page 1
Outline Representation of physical quantities The advection equation Conclusions Numerical …

2 Background Theories 3 2.1 Differential Geometry........................................ 3 2.1. 1
Manifold........................................... 3 2.1. 2 Differential Form...................................... 6 2.1. 3 …