Core Concepts
The paper derives a space-time variational formulation for the vectorial wave equation under consideration of Ohm's law, proves its unique solvability, and analyzes the discrete equivalent with a tensor product approach showing conditional stability.
Abstract
The paper focuses on developing the theoretical background for using space-time finite element methods to solve the vectorial wave equation, which is derived from Maxwell's equations.
Key highlights:
The vectorial wave equation is derived from Maxwell's equations in a space-time structure, taking into account Ohm's law.
A space-time variational formulation is derived for the vectorial wave equation using different trial and test spaces.
Unique solvability of the resulting Galerkin-Petrov variational formulation is proven.
The discrete equivalent of the equation in a tensor product form is analyzed, and a CFL condition for conditional stability is shown.
The goal is to improve the existing theory of Maxwell's equations and enable computations of more complicated electromagnetic problems.