Two other important criteria in the design of the library, unfortunately not @@ -483,15 +483,15 @@ is also used in teaching at the universities of Heidelberg and Minnesota.

+ SRC="next_motif.gif">

+ SRC="up_motif.gif">

+ SRC="previous_motif.gif">
Next: Grid handling diff --git a/deal.II/doc/reports/deal.II-paper/node2.html b/deal.II/doc/reports/deal.II-paper/node2.html index 29a899b6ed..502cfc8ab4 100644 --- a/deal.II/doc/reports/deal.II-paper/node2.html +++ b/deal.II/doc/reports/deal.II-paper/node2.html @@ -23,15 +23,15 @@ originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds

+ SRC="next_motif.gif">

+ SRC="up_motif.gif">

+ SRC="previous_motif.gif">
Next: Finite element spaces @@ -80,7 +80,7 @@ As has been outlined above, one of the design criteria was to focus on quadrilaterals in two, and hexahedra in three space dimensions. A triangulation is therefore made up of the objects in Figure

. + SRC="cross_ref_motif.gif">.

@@ -182,7 +182,7 @@ be noted that these constraints need not be incorporated using a Lagrangian multiplier (which would lead to saddle point problems), but can be inserted into the matrix and right hand side, thus retaining the properties of the matrices (cf. Section

). In + SRC="cross_ref_motif.gif">). In particular, symmetric and positive definite matrices retain these properties.

@@ -204,15 +204,15 @@ dramatic speed improvements compared with unstructured mesh approaches. + SRC="next_motif.gif"> + SRC="up_motif.gif"> + SRC="previous_motif.gif">
Next: Finite element spaces diff --git a/deal.II/doc/reports/deal.II-paper/node3.html b/deal.II/doc/reports/deal.II-paper/node3.html index 0f3516340f..927f3eeef2 100644 --- a/deal.II/doc/reports/deal.II-paper/node3.html +++ b/deal.II/doc/reports/deal.II-paper/node3.html @@ -23,15 +23,15 @@ originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds + SRC="next_motif.gif"> + SRC="up_motif.gif"> + SRC="previous_motif.gif">
Next: Iterative solvers @@ -67,7 +67,7 @@ this vector space. The functionals defining the degrees of freedom, for example the interpolation points of Lagrangian elements or face integrals for some nonconforming elements, may be associated with any of the basic topological objects of a mesh, as shown in Figure . The FiniteElement + SRC="cross_ref_motif.gif">. The FiniteElement class describing a certain finite element states the objects on which these functionals are defined. For neighboring cells, these nodes may coincide, in which case they are identified. @@ -77,7 +77,7 @@ In case of local refinement (h or p), an interface between two cel carry different node values, which we call hanging nodes. Then, additional compatibility conditions have to be imposed numerically, as we will explain below in Section . + SRC="cross_ref_motif.gif">.

@@ -218,7 +218,7 @@ cells of differing refinement, ¹ see Figure . The + SRC="cross_ref_motif.gif">. The degrees of freedom on the refined side of a face (for example the left side of the face with end points P₁ and P₂ in the figure) are not all matched by degrees of freedom on the coarse side, so in order to guarantee continuity @@ -395,7 +395,7 @@ bilinear shape functions the function $\varphi_1$ associated with node P₁in Figure can be written as + SRC="cross_ref_motif.gif"> can be written as u by the vector of its nodal values. For the grid in Figure and bilinear elements, + SRC="cross_ref_motif.gif"> and bilinear elements, the matrix C has the following form:

@@ -628,15 +628,15 @@ used the original matrix C.

+ SRC="next_motif.gif">

+ SRC="up_motif.gif">

+ SRC="previous_motif.gif">
Next: Iterative solvers diff --git a/deal.II/doc/reports/deal.II-paper/node4.html b/deal.II/doc/reports/deal.II-paper/node4.html index d2c10cf8b8..4ad4a7f2d1 100644 --- a/deal.II/doc/reports/deal.II-paper/node4.html +++ b/deal.II/doc/reports/deal.II-paper/node4.html @@ -23,15 +23,15 @@ originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds

+ SRC="next_motif.gif">

+ SRC="up_motif.gif">

+ SRC="previous_motif.gif">
Next: Example applications @@ -163,15 +163,15 @@ fragmentation of heap memory or to speed up allocation.

+ SRC="next_motif.gif">

+ SRC="up_motif.gif">

+ SRC="previous_motif.gif">
Next: Example applications diff --git a/deal.II/doc/reports/deal.II-paper/node5.html b/deal.II/doc/reports/deal.II-paper/node5.html index 5c11af13c7..b80afb778d 100644 --- a/deal.II/doc/reports/deal.II-paper/node5.html +++ b/deal.II/doc/reports/deal.II-paper/node5.html @@ -23,15 +23,15 @@ originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds

+ SRC="next_motif.gif">

+ SRC="up_motif.gif">

+ SRC="previous_motif.gif">
Next: Bibliography @@ -130,7 +130,7 @@ such as the Euler equations of inviscid, eventually transonic flow.

The examples in Figure of computations with locally + SRC="cross_ref_motif.gif"> of computations with locally refined grids for these equations were done by R. Hartmann. The left and middle picture show solutions of the nonlinear Burgers equation with two merging shocks on a coarse grid and a refined one; bilinear discontinuous @@ -240,7 +240,7 @@ indispensable.

In Figure we show two examples of estimated parameters + SRC="cross_ref_motif.gif"> we show two examples of estimated parameters along with the exact values. In order to reduce the degree of ill-posedness and to reduce the number of unknowns, the discretization of the parameter qwas performed on a coarser grid than the state variable u. In fact, the discretization was done on the same grid but we posed additional constraints @@ -303,7 +303,7 @@ obtained using the program described in [1,3]. In Figure , a wave traveling outward from the lower left corner of the + SRC="cross_ref_motif.gif">, a wave traveling outward from the lower left corner of the domain is shown. We used a simple error indicator to track the spreading of the wave to adjust the computational meshes accordingly; it can be seen that rather coarse cells were used where the solution is smooth. @@ -377,7 +377,7 @@ less cells, which enables us to use efficient multigrid algorithms.

Figure shows examples of solutions to Poisson's + SRC="cross_ref_motif.gif"> shows examples of solutions to Poisson's equation using Neumann boundary conditions on an embedded boundary curve. The interior of the circle is not part of the domain on which the problem is posed and the solution is set to zero there. @@ -408,15 +408,15 @@ the problem is posed and the solution is set to zero there. + SRC="next_motif.gif"> + SRC="up_motif.gif"> + SRC="previous_motif.gif">
Next: Bibliography diff --git a/deal.II/doc/reports/deal.II-paper/node6.html b/deal.II/doc/reports/deal.II-paper/node6.html index 4bfaf90921..6aaaeaa34e 100644 --- a/deal.II/doc/reports/deal.II-paper/node6.html +++ b/deal.II/doc/reports/deal.II-paper/node6.html @@ -23,15 +23,15 @@ originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds + SRC="next_motif.gif"> + SRC="up_motif.gif"> + SRC="previous_motif.gif">
Next: About this document ... diff --git a/deal.II/doc/reports/deal.II-paper/node7.html b/deal.II/doc/reports/deal.II-paper/node7.html index e4a55e8d49..ca4e99d02d 100644 --- a/deal.II/doc/reports/deal.II-paper/node7.html +++ b/deal.II/doc/reports/deal.II-paper/node7.html @@ -19,15 +19,15 @@ originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds + SRC="next_motif_gr.gif"> + SRC="up_motif.gif"> + SRC="previous_motif.gif">
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