The results agree with those in the literature.
The lower-order formulation typically overestimates the displacement for low levels of refinement,
while the higher-order interpolation scheme underestimates it, but be a lesser degree.
-This benchmark, and a series of others not shown here, give us conidence that the code is working
+This benchmark, and a series of others not shown here, give us confidence that the code is working
as it should
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A typical screen output generated by running the problem is shown below.
The particular case demonstrated is that of the $Q_2-DGPM_1-DGPM_1$ formulation.
It is clear that, using the Newton-Raphson method, quadratic convergence of the solution is obtained.
-Other than in the first timestep, solution convergence is achieved within 5 Newton increments.
+Other than in the first time step, solution convergence is achieved within 5 Newton increments.
The converged displacement's $L_2$-norm is several orders of magnitude less than the geometry scale.
@code
We then used ParaView to visualise the results for two cases.
The first was for the coarsest grid and the lowest-order interpolation method: $Q_1-DGPM_0-DGPM_0$.
-The seond was on a refined grid using a $Q_2-DGPM_1-DGPM_1$ formulation.
+The second was on a refined grid using a $Q_2-DGPM_1-DGPM_1$ formulation.
The vertical component of the displacement, the pressure $\widetilde{p}$ and the dilatation $\widetilde{J}$ fields
are shown below.
function in order to enforce a high degree of incompressibility in
materials. An additional Lagrange multiplier would be introduced,
but this could most easily be dealt with using the principle of
- augented Lagrange multipliers. This is demonstrated in <em>Simo and
+ augmented Lagrange multipliers. This is demonstrated in <em>Simo and
Taylor (1991) </em>.
- The constitutive relationship used in this
model is relatively basic. It may be beneficial to split the material