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7.15 Package FL.ELLSYS

This package contains the problem definition of systems of convection-diffusion-reaction equations. The system is given in the following form which is suited for a fixed-point iteration:

-div(a(x,u_old,nabla u_old) nabla u) + div(b(x,u_old,nabla u_old) u) + + c(x,u_old,nabla u_old) nabla u + + r(x,u_old,nabla u_old) u = f(x,u_old, nabla u_old) - div(g(x,u_old, nabla u_old)) - div(a(x,u_old,nabla u_old) h(x,u_old, nabla u_old))

where u:G to R^N. Note that the last two terms are introduced in the variational formulation and imply a natural Neumann boundary condition derivative{u}{n} = (g+a h) cdot n at boundaries where no Dirichlet constraints are posed.

Class: <ELLSYS-PROBLEM>

Systems of convection-diffusion-reaction equations. The coefficients should be vector-valued functions in this case.

Superclasses: <PDE-PROBLEM>

Function: ELLSYS-MODEL-PROBLEM DOMAIN COMPONENTS &KEY A B C D R F G H (DIRICHLET NIL DIRICHLET-P) INITIAL SIGMA EVP PROPERTIES DERIVED-CLASS

Generates a rather general elliptic problem on the given domain.

Function: ISOTROPIC-DIFFUSION DIM VALUES

Returns a sparse diagonal diffusion tensor with isotropic diffusion in each component. value should be a vector or a number and contains the amount of diffusion in each component.

Function: LINEARIZATION REACTION-JET

Returns a list of two functions namely u mapsto R(u)-DR(u)u and u mapsto -DR(u) which can be used directly in the discretization as source and reaction term.

Function: NR-OF-COMPONENTS PROBLEM

Returns the number of components for problem.