Finite volume

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Detailed Description

Collection of discretized finite volume operators.

This module comprises several methods to work with finite volume functions and provides a collection of discretized finite volume operators discretizing e.g. convection or diffusion terms in a parametrized partial differential equation.

Collaboration diagram for Finite volume:

Files
file	Contents.m
	FV.
file	fv_conv_diff_explicit_space.m
	fv_conv_diff_explicit_space(U,NU_ind,grid,model)
file	fv_conv_explicit_space.m
	fv_conv_explicit_space(U,NU_ind,grid,params) function applying an FV-space-discretization operator starting from old values U corresponding to the geometry given in grid producing a new vector of elementwise scalars NU but only on for the subelements with numbers given in NU_ind. If NU_ind is empty, all new values NU are determined, i.e. length(NU) = length(U) = grid.nelements
file	fv_conv_flux_matrix.m
	function computing the flux matrix of a convection problem. simply reformatting the grid data suitably for pointwise evaluation by conv_flux. As evaluation points the points of suitable gauss-quadratures are chosen. The degree can be chosen in the model structure.
file	fv_diff_explicit_space.m
	fv_diff_explicit_space(U,NU_ind,grid,params)
file	fv_element_mean.m
	function computing the element averages of a discrete function U in the grid elements with indices I. Most arguments are dummy, but required for more general discrete functions, e.g. p1, etc.
file	fv_frechet_operators_conv_flux_waterflow_upwind.m
	computes a jacobian of implicit non-linear convective contributions to time evolution matrices at a point (S,U).
file	fv_frechet_operators_diff_flux_pressure_gradient.m
	computes a jacobian of implicit non-linear convective contributions to time evolution matrices at a point (P,S).
file	fv_frechet_operators_diff_implicit_gradient.m
	computes a jacobian of implicit non-linear diffusion contributions to time evolution matrices at a point U.
file	fv_frechet_operators_diff_implicit_gradient2.m
	computes a jacobian of implicit non-linear diffusion contributions to time evolution matrices at a point U.
file	fv_frechet_operators_diff_implicit_gradient3.m
	computes a jacobian of implicit non-linear diffusion contributions to time evolution matrices at a point U.
file	fv_h1_inner_product_matrix.m
	function computing the h1 inner product matrix for fv-functions on the grid.
file	fv_implicit_space.m
	fv_implicit_space(model, model_data, U, [NU_ind])
file	fv_l2_error.m
	function computing the l2-error between the two fv-functions or function sequences in U1,U2.
file	fv_l2project.m
	func to the fv space. A quadrature of degree qdeg is used.
file	fv_linfty_error.m
	compute the infinity-norm error between two Dof vectors.
file	fv_num_conv_flux_engquist_osher.m
	Function computing a numerical convective Engquist-Osher flux matrix.
file	fv_num_conv_flux_lax_friedrichs.m
	Function computing a numerical convective Lax-Friedrichs flux matrix.
file	fv_num_diff_flux_gradient.m
	computes a numerical diffusive flux for a diffusion problem
file	fv_num_diff_flux_gradient_tensor.m
	computes a numerical diffusive flux for a diffusion problem including a tensor
file	fv_num_diff_flux_pressure_gradient.m
	computes a numerical diffusive flux for a diffusion problem
file	fv_operators_conv_explicit_engquist_osher.m
	computes convection contribution to finite volume time evolution matrices, or their Frechet derivative
file	fv_operators_conv_explicit_lax_friedrichs.m
	computes convection contribution to finite volume time evolution matrices, or their Frechet derivative
file	fv_operators_conv_flux_waterflow_upwind.m
	computes convection contribution to finite volume time evolution matrices, or their Frechet derivative
file	fv_operators_diff_implicit_gradient.m
	computes diffusion contributions to finite volume time evolution matrices, or their Frechet derivative
file	fv_operators_diff_implicit_gradient2.m
	computes diffusion contributions to finite volume time evolution matrices, or their Frechet derivative
file	fv_operators_neumann_explicit.m
	computes a neumann contribution matrix for finite volume time evolution operators, or their Frechet derivative
file	fv_operators_output.m
	function returning components, coefficients, and complete operator for a linear output functional on fv discrete functions
file	fv_plot.m
	routine plotting a single fv function of fv_functions.
file	fv_space_operator.m
	fv_space_operator(model,model_data,U,NU_ind,grid,weights)