mkDirBC(DBCeq, unknown_list, old_unknown_list, params_list, bsf_file)

Parameters:

DBCeq - A list of equations specifying Dirichlet boundary conditions. Each entry in the list is an equation of the form u(x,y)=expr, where u(x,y) is a variable in unknown_list. For those variables in unknown_list, which do not appear in DBCeq, a default Dirichlet boundary condition is used. This is u(x,y) = qBCval, where qBCval is a predefined value which is specified with the mesh.
If one of the entries in DBCeq is SinglePoint(var), where var is one of the variables in unknown_list, a Dirichlet condition is applied at one single node, prescribing the variable to be zero at that node.

unknown_list - The list of unknowns as discussed above.

old_unknown_list - The list of unknowns at the previous timestep, as discussed above.

params_list - A list of scalar input parameters.

bsf_file - A file containing a Maple description of a particular finite element.

• Generates the code needed to specify Dirichlet boundary conditions.
• If the string 'qBCval' is encountered in DBCeq, it is replaced by a predefined value specified with the mesh. This gives a way of separating parts of the boundary with different Dirichlet conditions.
• If one of the entries in DBCeq is SinglePoint(var), the value of that variable will be set to zero at one single node. This is useful for equations with only Neumann conditons, for which the solution is only determined up to an additive constant. Using SinglePoint(var) this additive constant is fixed (arbitrarily), and possible numerical problems are avoided.

Examples:

> # set up lists:
> eq_list:= [ueq,veq,peq]:
> unknown_list:= [u(x,y),v(x,y),p(x,y)]:
> old_unknown_list:= [uo(x,y),vo(x,y),po(x,y)]:
> params_list:= [Diffusivity,bigQ,BCpara]:
> # Dirichlet BCs;
> # The call below creates the following boundary conditions:
# u(x,y)=x*BCpara on Dirichlet parts of the boundary, ;
# v(x,y)=qBCval on Dirichlet parts of the boundary;
# p(x,y)=0 at one single node;
> DBCueq:= u(x,y)=x*BCpara:
> mkDirBC([DBCueq,SinglePoint(p(x,y))],unknown_list,
old_unknown_list,params_list,`2DP1_gsq_bsf`):