## Re: [Libmesh-users] Lagrange DG basis

 Re: [Libmesh-users] Lagrange DG basis From: John Peterson - 2012-02-07 00:46:24 ```On Mon, Feb 6, 2012 at 4:36 PM, David Knezevic wrote: > On 02/06/2012 06:09 PM, John Peterson wrote: >> >> On Mon, Feb 6, 2012 at 3:24 PM, David Knezevic >>  wrote: >>> >>> Hi all, >>> >>> I'd like to use a DG version of the Lagrange shape functions. This is >>> pursued, for example, in the book "Nodal Discontinuous Galerkin Methods" >>> by Hesthaven and Warburton. >> >> What's the main motivation for using the Lagrange basis?  Better >> conditioning than monomials? > > > I'd like to compare to a Matlab DG code which uses (or will use) these > L2_LAGRANGE basis functions. These basis functions are important in Matlab > because with, say, MONOMIALs, you need to do an L^2 projection to represent > f(u_h) in the FE space. The element loop to assemble the right-hand side for > this projection appears to be a bottleneck in Matlab, especially if you have > to do it every timestep. With L2_LAGRANGE you can do interpolation instead > of projection. Oh, that sounds like a good idea actually... > Also, yep, conditioning of L2_LAGRANGE will be better than MONOMIALs for the > same order shape functions. But (L2_)LAGRANGE only goes up to cubic and the > condition number for cubic MONOMIALs isn't too bad. We could probably add higher orders too if this is determined to be useful... I assume you can directly call the continuous LAGRANGE shape() and shape_deriv() functions for the discontinuous family? -- John ```