Discontinuous Galerkin methods Lecture 3 - Brown University

2.4 Interlude on linear hyperbolic problems
For But linear systems, first a the bit construction more of on thefluxes upwind numerical flux is particularly
simple and we will discuss this in a bit more detail. Important application
areas include Maxwell’s equations and the equations of acoustics and
elasticity. Let us briefly look a little more carefully at linear
To systems illustrate the basic approach, let us consider the two-dimensional
system
Q(x) ∂u
+ ∇ ·F = Q(x)∂u
∂t ∂t + ∂F 1
∂x + ∂F linear systems, the construction of the upwind numerical flux is particrly
simple and we will discuss this in a bit more detail. Important appliion
areas include Maxwell’s equations and the equations of acoustics and
sticity.
To illustrate the basic approach, let us consider the two-dimensional
tem
Q(x)
2
=0, (2.19)
∂y
where the flux is assumed to be given as
F =[F1, F 2] =[A1(x)u, A2(x)u] .
Furthermore, we will make the natural assumption that Q(x) is invertible and
symmetric for all x ∈ Ω. To formulate the numerical flux, we will need an
∂u
+ ∇ ·F = Q(x)∂u
∂t ∂t + ∂F 1
∂x + ∂F 2
=0, (2.19)
∂y
ere the flux is assumed to be given as
F =[F1, F 2] =[A1(x)u, A2(x)u] .
thermore, Prominent we will make examples the natural areassumption
that Q(x) is invertible and
metric • Acoustics
for all x ∈ Ω. To formulate the numerical flux, we will need an
• Electromagnetics
• Elasticity
In such cases we can derive exact upwind fluxes