Discontinuous Galerkin methods Lecture 1 - Brown University
Discontinuous Galerkin methods Lecture 1 - Brown University
Discontinuous Galerkin methods Lecture 1 - Brown University
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n June 7, 2006 9:29<br />
Why high-order accuracy ?<br />
Let us first define a high-order method as one having<br />
a truncation order exceeding 2<br />
From local to global approximation<br />
Let us consider a simple time-dependent problem<br />
ample 1.1 Consider the wave equation<br />
∂u<br />
∂t<br />
= −2π ∂u<br />
∂x<br />
u(x, 0) = e sin(x) ,<br />
0 ≤ x ≤ 2π, (1.1)<br />
h periodic boundary conditions.<br />
The We exactshall solution solve to Equation it using (1.1) two isdifferent a right-moving ways wave of the form<br />
u(x, t) = e sin(x−2πt) • A standard 2nd order finite difference method<br />
,<br />
• A Fourier spectral method - an ‘infinite order’ method<br />
, the initial condition is propagating with a speed 2π.
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