README.md

k = 3: The Dirichlet Problem for the Axisymmetric Poisson Equation

Usage

Syntax

To compare a known exact solution u and to its approximated solution:

[err] = weighted_HL_k_3_e(f_vec_r,f_vec_th,f_vec_z,gd,sf,ns,mesh,z_vec_r,z_vec_th,z_vec_z,p_exact,n)

To find the approximated solution to an unknown solution:

[basis_edges,basis_triangles,z_h,p_h] = weighted_HL_k_3(f,gd,sf,ns,mesh,n)

Inputs

f - given function gd,sf,ns - outputs of pdepoly specifying domain mesh - max mesh level z_vec_r - exact solution z vector r component z_vec_th - exact solution z vector theta component z_vec_z - exact solution z vector z component p_vec_r - exact solution p vector r component p_vec_th - exact solution p vector theta component p_vec_z - exact solution p vector z component

Outputs

err_z - array of L2 errors for mesh levels corresponding to indices err_p - array of L2 errors for mesh levels corresponding to indices
basis_edges - a matrix representing piece-wise basis functions for each edge in each triangle. basis(i,:,T) represents the pieceiwise basis function for the ith edge in triangle T.
basis_triangles - a vector representing piece-wise basis functions for edge triangle. basis(1,T) represents the piecewise basis function for the Tth triangle.
z_h - approximated solution vector for z
p_h - approximated solution vector for p

Example

% add path for get_data_1() function
addpath ../data/
% define the highest mesh level
mesh = 5;
% define the nth-Fourier mode
n = 1;
% define the problem domain
pdepoly([0,1,1,0], [0,0,1,1]);
% define the equations
[z_vec_r,z_vec_th,z_vec_z,p_exact,f] = get_data_1(n);
% run the program
[err_z,err_p] = weighted_HL_k_3_e(f,gd,sf,ns,mesh,z_vec_r,z_vec_th,z_vec_z,p_exact,n)

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