(w, f)_{\mathcal{T}},
\quad \forall w \in \mathcal{W}_h^p,
\\
- < \mu, \mathbf{c} \lambda_h\cdot \mathbf{n}
+ \left< \mu, \mathbf{c} \lambda_h\cdot \mathbf{n}
+ \mathbf{q}_h\cdot \mathbf{n}
- + \tau (u_h - \lambda_h)>_{\partial \mathcal{T}}
+ + \tau (u_h - \lambda_h)\right>_{\partial \mathcal{T}}
&=&
- <\mu, g_N>_{\partial\Omega_N},
+ \left<\mu, g_N\right>_{\partial\Omega_N},
\quad \forall \mu \in \mathcal{M}_h^p.
@f}
improvement makes most sense.
<ol>
- <li> Better linear solvers: We use a GMRES iterative solver without
+ <li> Better linear solvers: We use a BiCGStab iterative solver without
preconditioner, where the number of iteration increases with increasing
problem size (the number of iterations for Q1 elements and global
- refinements start at 8 for the small sizes but increase up to 2592 for the
+ refinements start at 35 for the small sizes but increase up to 701 for the
largest size). To do better, one could for example use an algebraic
multigrid preconditioner from Trilinos. For diffusion-dominated problems as
the problem at hand with finer meshes, such a solver can be designed that
<li> Speed up assembly by pre-assembling parts that do not change from one
cell to another (those that do neither contain variable coefficients nor
- mapping-dependent terms.
+ mapping-dependent terms).
</ol>