diff --git a/find_edge_connectivity.m b/find_edge_connectivity.m index 6f9bf48..650c18a 100644 --- a/find_edge_connectivity.m +++ b/find_edge_connectivity.m @@ -1,5 +1,5 @@ function [t_ed] = find_edge_connectivity(t,ed,mesh) -% FIND_EDGES - Find the edges in each triangulation in the mesh +% FIND_EDGE_CONNECTIVITY - Find the edges in each triangulation in the mesh % % Syntax: % [ed, t_ed] = find_edges(t) @@ -20,7 +20,9 @@ % Date: Fall 2020 if exist('mesh','var') - % mesh is given + % if mesh is given + % determine if we have saved a matrix for the given mesh & domain to + % save computational time if mesh == 6 && isfile('edge_resources/t_ed_6.mat') t_ed_6 = load('edge_resources/t_ed_6.mat'); t_ed = t_ed_6.t_ed_6; diff --git a/k_0/data/get_data1.m b/k_0/data/get_data1.m index 6f1a7fa..e43ceab 100644 --- a/k_0/data/get_data1.m +++ b/k_0/data/get_data1.m @@ -4,6 +4,8 @@ % data1 % u = (1/3)r^3 - (1/2)r^2 % f = -(8/3)r + (5/2) +% Author: Nicole Stock +% Date: Fall 2020 f = @(r,z) -(8./3).*r + (3./2); grad_f_r =@(r,z) -8./3; diff --git a/k_0/data/get_data2.m b/k_0/data/get_data2.m index d0c0251..fc3507e 100644 --- a/k_0/data/get_data2.m +++ b/k_0/data/get_data2.m @@ -4,6 +4,8 @@ % data2 % u = r^3 - (3/2)r^2 % f = -8r + 9/2 +% Author: Nicole Stock +% Date: Fall 2020 f = @(r,z) -8.*r + (9./2); grad_f_r =@(r,z) -8; diff --git a/k_0/data/get_data3.m b/k_0/data/get_data3.m index fad2cae..526cadc 100644 --- a/k_0/data/get_data3.m +++ b/k_0/data/get_data3.m @@ -2,6 +2,8 @@ %GET_U_DATA3 Get u and f function handles % % u = r^(1/2) +% Author: Nicole Stock +% Date: Fall 2020 u = @(r,z) r.^(1./2); grad_u_r =@(r,z) (1./2).*r.^(-1./2); diff --git a/k_0/data/get_data4.m b/k_0/data/get_data4.m index fbeeeda..aa3dffb 100644 --- a/k_0/data/get_data4.m +++ b/k_0/data/get_data4.m @@ -2,6 +2,8 @@ %GET_U_DATA4 Get u and f function handles % % u = r^(2/3) +% Author: Nicole Stock +% Date: Fall 2020 u = @(r,z) r.^(2./3); grad_u_r =@(r,z) (2./3).*r.^(-1./3); diff --git a/k_0/data/get_data5.m b/k_0/data/get_data5.m index aadaea0..c365a06 100644 --- a/k_0/data/get_data5.m +++ b/k_0/data/get_data5.m @@ -2,6 +2,8 @@ %GET_U_DATA5 Get u and f function handles % % u = r^(5/6) +% Author: Nicole Stock +% Date: Fall 2020 u = @(r,z) r.^(5./6); grad_u_r =@(r,z) (5./6).*r.^(-1./6); diff --git a/k_0/data/get_data6.m b/k_0/data/get_data6.m index a18446b..916954d 100644 --- a/k_0/data/get_data6.m +++ b/k_0/data/get_data6.m @@ -2,6 +2,8 @@ %GET_U_DATA6 Get u and f function handles % % u = r*sin(z) +% Author: Nicole Stock +% Date: Fall 2020 u = @(r,z) r.*sin(z); grad_u_r =@(r,z) sin(z); diff --git a/k_0/data/get_data7.m b/k_0/data/get_data7.m index 3896adf..a703abb 100644 --- a/k_0/data/get_data7.m +++ b/k_0/data/get_data7.m @@ -2,6 +2,8 @@ %GET_U_DATA7 Get u and f function handles % % u = r^(1/3) +% Author: Nicole Stock +% Date: Fall 2020 u = @(r,z) r.^(1./3); grad_u_r =@(r,z) (1./3).*r.^(-2./3); diff --git a/k_0/data/get_data8.m b/k_0/data/get_data8.m index 20d3df9..4d18721 100644 --- a/k_0/data/get_data8.m +++ b/k_0/data/get_data8.m @@ -2,6 +2,8 @@ %GET_U_DATA8 Get u and f function handles % data3 % u = r^(4/3) +% Author: Nicole Stock +% Date: Fall 2020 u = @(r,z) r.^(4./3); grad_u_r =@(r,z) (4./3).*r.^(1./3); diff --git a/k_0/data/get_data9.m b/k_0/data/get_data9.m index f071539..bfea00f 100644 --- a/k_0/data/get_data9.m +++ b/k_0/data/get_data9.m @@ -1,6 +1,8 @@ function [f,grad_f_r,grad_f_z,u,grad_u_r,grad_u_z] = get_data9() %GET_U_DATA9 Get u and f function handles % u = r^(5/3) +% Author: Nicole Stock +% Date: Fall 2020 u = @(r,z) r.^(5./3); grad_u_r =@(r,z) (5./3).*r.^(2./3); diff --git a/k_0/p1/basis_functions_weighted_HL_k_0_p1.m b/k_0/p1/basis_functions_weighted_HL_k_0_p1.m index 2b008f2..0110597 100644 --- a/k_0/p1/basis_functions_weighted_HL_k_0_p1.m +++ b/k_0/p1/basis_functions_weighted_HL_k_0_p1.m @@ -14,7 +14,7 @@ % % Outputs: % basis - a matrix representing piece-wise basis functions for each node -% in each triangle. basis(i,:,T) represents the pieceiwise basis +% in each triangle. basis(:,i,T) represents the pieceiwise basis % function for the ith node in triangle T. % % Author: Nicole Stock diff --git a/k_1/data/get_data_1.m b/k_1/data/get_data_1.m index 47ae8b2..8137a33 100644 --- a/k_1/data/get_data_1.m +++ b/k_1/data/get_data_1.m @@ -8,6 +8,9 @@ % f = [ -15r^2 + 8r + n^2r^2 - n^2r % 2nr^2 - 2nr % 0 ] +% Author: Nicole Stock +% Date: Fall 2020 + u_vec_r = @(r,z) r.^4 - r.^3; u_vec_th = @(r,z) 0; u_vec_z = @(r,z) 0; diff --git a/k_1/lowest_order/create_B_weighted_HL_k_1_p1.m b/k_1/lowest_order/create_B_weighted_HL_k_1_p1.m index 07c23a7..3649856 100644 --- a/k_1/lowest_order/create_B_weighted_HL_k_1_p1.m +++ b/k_1/lowest_order/create_B_weighted_HL_k_1_p1.m @@ -1,6 +1,6 @@ function B = create_B_weighted_HL_k_1_p1(p,t,ed,t_ed,basis_nodes,basis_edges,n) % CREATE_B_WEIGHTED_HL_K_1_P1 - Create B matrix -% Hodge Laplacian k = 1 case, P1 +% Hodge Laplacian k = 1 case, lowest order % (grad_rz^n(phi_i), zeta_j)_r where {phi_k}k=1->N is the basis for Ah % and {zeta_l}l=1->N+Ne is the basis for Bh % (Ah is the weighted P1 space) @@ -55,7 +55,7 @@ [R,Z,Wr,Wz] = triquad(7, coordinates); - % integrate for each pair of edges + 1 in the triangle + % integrate for each pair of basis functions in the triangle for i = 1:3 for j = 1:6 I = basis_nodes(:,i,T); diff --git a/k_1/lowest_order/create_F_weighted_HL_k_1_p1.m b/k_1/lowest_order/create_F_weighted_HL_k_1_p1.m index 8f0014b..0ae34b4 100644 --- a/k_1/lowest_order/create_F_weighted_HL_k_1_p1.m +++ b/k_1/lowest_order/create_F_weighted_HL_k_1_p1.m @@ -30,7 +30,7 @@ % weight % % Outputs: -% S - S matrix used to solve system of equations to approximate +% F - F matrix used to solve system of equations to approximate % solution % % Author: Nicole Stock diff --git a/k_1/lowest_order/create_S_weighted_HL_k_1_p1.m b/k_1/lowest_order/create_S_weighted_HL_k_1_p1.m index cead11e..68180ad 100644 --- a/k_1/lowest_order/create_S_weighted_HL_k_1_p1.m +++ b/k_1/lowest_order/create_S_weighted_HL_k_1_p1.m @@ -54,7 +54,7 @@ [R,Z,Wr,Wz] = triquad(7, coordinates); - % integrate for each pair of edges + 1 in the triangle + % integrate for each pair of basis functions in the triangle for i = 1:6 for j = i:6 if i <=3 diff --git a/k_1/lowest_order/errors_exact_weighted_HL_k_1_p1.m b/k_1/lowest_order/errors_exact_weighted_HL_k_1_p1.m index 1770a4f..37e2e04 100644 --- a/k_1/lowest_order/errors_exact_weighted_HL_k_1_p1.m +++ b/k_1/lowest_order/errors_exact_weighted_HL_k_1_p1.m @@ -4,7 +4,7 @@ % Hodge Laplacian k = 1 case, P1 % % Syntax: -% [err,grad_err,max_err] = +% [err_u,err_s] = % errors_exact_weighted_HL_k_1_p1 % Inputs: % p - a 2xNumNodes matrix representing nodal coordinates. diff --git a/k_1/lowest_order/weighted_HL_k_1_e.m b/k_1/lowest_order/weighted_HL_k_1_e.m index ab79107..df7a713 100644 --- a/k_1/lowest_order/weighted_HL_k_1_e.m +++ b/k_1/lowest_order/weighted_HL_k_1_e.m @@ -1,9 +1,9 @@ function [err_u,err_s] = weighted_HL_k_1_e(f_vec_r,f_vec_th,f_vec_z,gd,sf,ns,mesh,u_vec_r,u_vec_th,u_vec_z,s,n) -%WEIGHTED_HL_K_1_E Hodge Laplacian k = 1 P1 Finite Element Method. +%WEIGHTED_HL_K_1_E Hodge Laplacian k = 1 lowest order Finite Element Method. % This program is set up to be given an exact solution. -% Hodge Laplacian k = 1 case, P1 -% {phi_i}i=1->N is the basis for Ah -% {zeta_j}j=1->N+Ne is the basis for Bh +% Hodge Laplacian k = 1 case, lowest order +% {phi_i}i=1->N is the basis for Ah0 +% {zeta_j}j=1->N+Ne is the basis for Bh0 % (Ah is the weighted P1 space) % (Bh is the weighted fourier modified Nedelec and P1 space) % Solve for (s,u) in (Ah x Bh) s.t. @@ -14,6 +14,8 @@ % % Syntax: % [err] = weighted_HL_k_1_e(f_vec_r,f_vec_th,f_vec_z,gd,sf,ns,mesh,u_vec_r,u_vec_th,u_vec_z,s,n) +% +% Inputs: % f_vec_r - given function r component % f_vec_th - given function theta component % f_vec_z - given function z component @@ -31,11 +33,11 @@ % Usage Exampled: % addpath ../../data ../data/ % n = 1; -% [u_vec_r,u_vec_th,u_vec_z,s,f_vec_r,f_vec_th,f_vec_z] = get_data_1(n) +% [u_vec_r,u_vec_th,u_vec_z,s,f_vec_r,f_vec_th,f_vec_z] = get_data_1(n); % mesh = 7; % pdepoly([0,1,1,0], [0,0,1,1]); % (OR) [gd,sf,ns] = get_gd_sf_ns([0,1,1,0],[0,0,1,1]); -% [err_u,err_s] = weighted_HL_k_1_e(f_vec_r,f_vec_th,f_vec_z,gd,sf,ns,mesh,u_vec_r,u_vec_th,u_vec_z,s,n) +% [err_u,err_s] = weighted_HL_k_1_e(f_vec_r,f_vec_th,f_vec_z,gd,sf,ns,mesh,u_vec_r,u_vec_th,u_vec_z,s,n); % Dependencies: % find_edge_connectivity.m % basis_functions_weighted_modified_nedelec_and_p1.m @@ -52,6 +54,7 @@ addpath('../../'); addpath('../../modified_weighted_nedelec_pk/p1/'); addpath('../../nedelec/weighted_lowest_order/') +addpath('../../k_0/p1/'); model=createpde(1); g=decsg(gd,sf,ns); diff --git a/k_2/data/get_data_1.m b/k_2/data/get_data_1.m index e52b7dc..0688d69 100644 --- a/k_2/data/get_data_1.m +++ b/k_2/data/get_data_1.m @@ -10,6 +10,8 @@ % f = [ 3n^2 - (3n^2)/r + 6n - (4n)/r - 9 % -3n^2 + (2n^2)/r - 6n + (6n)/r + 9 % 0 ] +% Author: Nicole Stock +% Date: Fall 2020 s_vec_r = @(r,z) 3.*r.*(r-1); % 3.*r.^2 - 3.*r s_vec_th = @(r,z) -3.*r.^2 + 2.*r; diff --git a/k_2/lowest_order/create_F_weighted_HL_k_2_p1.m b/k_2/lowest_order/create_F_weighted_HL_k_2_p1.m index fbbbd7d..d4ff4fc 100644 --- a/k_2/lowest_order/create_F_weighted_HL_k_2_p1.m +++ b/k_2/lowest_order/create_F_weighted_HL_k_2_p1.m @@ -29,7 +29,7 @@ % f_vec_z - given function z component % % Outputs: -% S - S matrix used to solve system of equations to approximate +% F - F matrix used to solve system of equations to approximate % solution % % Author: Nicole Stock @@ -87,4 +87,4 @@ F = sparse(i_vec,j_vec,s_vec,edges+triangles,1); -% end \ No newline at end of file +% end diff --git a/k_2/lowest_order/create_S_weighted_HL_k_2_p1.m b/k_2/lowest_order/create_S_weighted_HL_k_2_p1.m index aef17d7..95fe2dd 100644 --- a/k_2/lowest_order/create_S_weighted_HL_k_2_p1.m +++ b/k_2/lowest_order/create_S_weighted_HL_k_2_p1.m @@ -1,6 +1,6 @@ function S = create_S_weighted_HL_k_2_p1(p,t,ed,t_ed,basis_RT_edges,basis_triangles) % CREATE_S_WEIGHTED_HL_K_2_P1 - Create S matrix -% Hodge Laplacian k = 2 case, P1 +% Hodge Laplacian k = 2 case, lowest order % (div_rz^n(psi_i), div_rz^n(psi_j))_r where {psi_j}j=1->Ne+Nt is the basis for Ch % (Ch is the weighted fourier Raviart Thomas space) % @@ -26,7 +26,7 @@ % function for the Tth triangle. % % Outputs: -% B - B matrix used to solve system of equations to approximate +% S - S matrix used to solve system of equations to approximate % solution % % Author: Nicole Stock @@ -99,4 +99,4 @@ S = sparse(i_vec,j_vec,s_vec,edges+triangles,edges+triangles); -% end \ No newline at end of file +% end diff --git a/k_2/lowest_order/mass_matrix_weighted_HL_k_2_p1.m b/k_2/lowest_order/mass_matrix_weighted_HL_k_2_p1.m index fdf05d2..54e6c09 100644 --- a/k_2/lowest_order/mass_matrix_weighted_HL_k_2_p1.m +++ b/k_2/lowest_order/mass_matrix_weighted_HL_k_2_p1.m @@ -1,6 +1,6 @@ function mass_matrix = mass_matrix_weighted_HL_k_2_p1(p,t,ed,t_ed,basis_nodes,basis_edges,n) % MASS_MATRIX_WEIGHTED_HL_K_2_P1 - Create mass matrix -% Hodge Laplacian k = 2 case, P1 +% Hodge Laplacian k = 2 case, lowest order % (zeta_i, zeta_j)_r where {zeta_k}k=1->(N+Ne) is the basis for Bh % (Bh is the weighted fourier modified Nedelec and P1 space) % @@ -112,4 +112,4 @@ end mass_matrix = sparse(i_vec,j_vec,s_vec,nodes+edges,nodes+edges); -% end \ No newline at end of file +% end diff --git a/k_2/lowest_order/weighted_HL_k_2_e.m b/k_2/lowest_order/weighted_HL_k_2_e.m index 3181214..993134c 100644 --- a/k_2/lowest_order/weighted_HL_k_2_e.m +++ b/k_2/lowest_order/weighted_HL_k_2_e.m @@ -1,9 +1,9 @@ function [err_u,err_s] = weighted_HL_k_2_e(f_vec_r,f_vec_th,f_vec_z,gd,sf,ns,mesh,u_vec_r,u_vec_th,u_vec_z,s_vec_r,s_vec_th,s_vec_z,n) -%WEIGHTED_HL_K_1_E Hodge Laplacian k = 1 P1 Finite Element Method. +%WEIGHTED_HL_K_2_E Hodge Laplacian k = 2 lowest order Finite Element Method. % This program is set up to be given an exact solution. -% Hodge Laplacian k = 2 case, P1 -% {zeta_j}j=1->N+Ne is the basis for Bh -% {psi_i}i=1->Ne+Nt is the basis for Ch +% Hodge Laplacian k = 2 case, lowest order +% {zeta_j}j=1->N+Ne is the basis for Bh0 +% {psi_i}i=1->Ne+Nt is the basis for Ch0 % (Bh is the weighted fourier modified Nedelec and P1 space) % (Ch is the weighted fourier Raviart Thomas space) % Solve for (s,u) in (Bh x Ch) s.t. diff --git a/k_3/lowest_order/errors_exact_weighted_HL_k_3_p1.m b/k_3/lowest_order/errors_exact_weighted_HL_k_3_p1.m index cfa91c6..47978a1 100644 --- a/k_3/lowest_order/errors_exact_weighted_HL_k_3_p1.m +++ b/k_3/lowest_order/errors_exact_weighted_HL_k_3_p1.m @@ -93,9 +93,7 @@ % find L2 Error for p integrand =@(r,z) ((p_exact(r,z) - p_h(T)).^2).*r; - integral_p = integral_p + Wx'*feval(integrand,X,Y)*Wy; - - + integral_p = integral_p + Wx'*feval(integrand,X,Y)*Wy; end err_z = sqrt(integral_z); diff --git a/k_3/lowest_order/weighted_HL_k_3_e.m b/k_3/lowest_order/weighted_HL_k_3_e.m index bb4db29..4973104 100644 --- a/k_3/lowest_order/weighted_HL_k_3_e.m +++ b/k_3/lowest_order/weighted_HL_k_3_e.m @@ -1,9 +1,9 @@ function [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) -%WEIGHTED_HL_K_3_E Hodge Laplacian k = 3 P1 Finite Element Method. +%WEIGHTED_HL_K_3_E Hodge Laplacian k = 3 lowest order Finite Element Method. % This program is set up to be given an exact solution. -% Hodge Laplacian k = 3 case, P1 -% {psi_i}i=1->Ne+Nt is the basis for Ch -% {chi_j}j=1->Nt is the basis for Dh +% Hodge Laplacian k = 3 case, lowest order +% {psi_i}i=1->Ne+Nt is the basis for Ch0 +% {chi_j}j=1->Nt is the basis for Dh0 % (Ch is the weighted fourier Raviart Thomas space) % (Dh is the piecewise constant space) % Solve for (z,p) in (Ch x Dh) s.t. diff --git a/modified_weighted_nedelec_pk/data/p1/get_data_1.m b/modified_weighted_nedelec_pk/data/p1/get_data_1.m index 5c5b157..a08c97f 100644 --- a/modified_weighted_nedelec_pk/data/p1/get_data_1.m +++ b/modified_weighted_nedelec_pk/data/p1/get_data_1.m @@ -6,6 +6,8 @@ % F = [ n(r-1) + u_r ] % [ -2r + 1 + u_th ] % [ u_z ] +% Author: Nicole Stock +% Date: Fall 2020 u_vec_r = @(r,z) z - (1./n).*((1./3).*r.^3 - (1./2).*r.^2); u_vec_th = @(r,z) (-1).*n.*z + (1./3).*r.^3 - (1./2).*r.^2; diff --git a/nedelec/data/weighted/get_data_1.m b/nedelec/data/weighted/get_data_1.m index 9cb3fa1..f5ab18b 100644 --- a/nedelec/data/weighted/get_data_1.m +++ b/nedelec/data/weighted/get_data_1.m @@ -2,6 +2,8 @@ %GET_DATA_1 Get u vector and f vector % u = [ sin(pi*r) ; cos(pi*r) ] % F = u +% Author: Nicole Stock +% Date: Fall 2020 u_vec_r = @(r,z) sin(pi.*r); u_vec_z = @(r,z) cos(pi.*z); diff --git a/nedelec/data/weighted/get_data_2.m b/nedelec/data/weighted/get_data_2.m index 2c2c593..5f4184e 100644 --- a/nedelec/data/weighted/get_data_2.m +++ b/nedelec/data/weighted/get_data_2.m @@ -4,6 +4,8 @@ % (1/2)r^2z - rz ] % F = [ (1/3)rz^3 - (1/3)z^3 - 2rz + 2z + r - 1 % 2z^2 - (z^2)/r + (1/2)r^2z - rz - 2z + z/r ] +% Author: Nicole Stock +% Date: Fall 2020 u_vec_r =@(r,z) (1/3).*(r-1).*z.^3; u_vec_z =@(r,z) (1/2).*r.^2.*z - r.*z; diff --git a/nedelec/data/weighted/get_data_3.m b/nedelec/data/weighted/get_data_3.m index 012f83d..476632d 100644 --- a/nedelec/data/weighted/get_data_3.m +++ b/nedelec/data/weighted/get_data_3.m @@ -4,6 +4,8 @@ % (-1/2)r^2z^2 + rz^2 ] % F = [ (-1/2)rz^2 + (1/2)z^2 - 2rz + 2z + r - 1 % (-1/2)r^2z^2 + rz^2 + 2z^2 - z^2/r - 2z + z/r ] +% Author: Nicole Stock +% Date: Fall 2020 u_vec_r =@(r,z) (-1/2).*r.*z.^2 + (1./2).*z.^2; u_vec_z =@(r,z) (-1/2).*r.^2.*z.^2 + r.*z.^2; diff --git a/raviart_thomas/data/unweighted2D/get_data_1.m b/raviart_thomas/data/unweighted2D/get_data_1.m index 7647b5c..5a8ba27 100644 --- a/raviart_thomas/data/unweighted2D/get_data_1.m +++ b/raviart_thomas/data/unweighted2D/get_data_1.m @@ -4,6 +4,8 @@ % -(1/2)r^2z^2 + (1/2)rz^2 ] % F = [ (1/3)r^3z^2 - (1/2)r^2z^2 - 2rz^2 + z^2 + 2rz - z % -(1/2)r^2z^2 + (1/2)rz^2 - 2r^2z + 2rz + r^2 - r ] +% Author: Nicole Stock +% Date: Fall 2020 u_vec_r = @(r,z) (1./3).*(r.^3).*(z.^2) - (1./2).*(r.^2).*(z.^2); u_vec_z = @(r,z) -(1./2).*(r.^2).*(z.^2) + (1./2).*r.*z.^2; diff --git a/raviart_thomas/data/unweighted2D/get_data_2.m b/raviart_thomas/data/unweighted2D/get_data_2.m index e5e79ea..0c90157 100644 --- a/raviart_thomas/data/unweighted2D/get_data_2.m +++ b/raviart_thomas/data/unweighted2D/get_data_2.m @@ -4,6 +4,8 @@ % -(1/3)rz^3 + (1/2)rz^2 ] % F = [ (1/3)r^3z^2 - (1/3)r^3z - 2rz^2 + z^2 + 2rz - z % -(1/3)rz^3 + (1/2)rz^2 - 2r^2z + 2rz + r^2 - r ] +% Author: Nicole Stock +% Date: Fall 2020 u_vec_r = @(r,z) (1./3).*(r.^3).*(z.^2) - (1./3).*z.*r.^3; u_vec_z = @(r,z) -(1./3).*r.*z.^3 + (1./2).*r.*z.^2; diff --git a/raviart_thomas/data/weighted/get_data_1.m b/raviart_thomas/data/weighted/get_data_1.m index 9ca44d0..c41b704 100644 --- a/raviart_thomas/data/weighted/get_data_1.m +++ b/raviart_thomas/data/weighted/get_data_1.m @@ -6,6 +6,8 @@ % F = [ -rz^2 - z^2 + z % -(n/r)(rz^2 - z^2 - rz + z) % (1/3)rz^3 - (1/2)rz^2 + (1/2)z^2 + (1/3)z^3 - 2rz + 2z + r - 1 ] +% Author: Nicole Stock +% Date: Fall 2020 u_vec_r = @(r,z) -r.*z.^2; u_vec_th = @(r,z) 0; diff --git a/raviart_thomas/data/weighted/get_data_2.m b/raviart_thomas/data/weighted/get_data_2.m index 0467257..85b4d67 100644 --- a/raviart_thomas/data/weighted/get_data_2.m +++ b/raviart_thomas/data/weighted/get_data_2.m @@ -6,6 +6,8 @@ % F = [ (1/2)rz - (1/2)rz^2 - z^2 + z % -(n/r)(rz^2 - z^2 - rz + z) % (1/3)rz^3 - (1/2)rz^2 -2rz + 2z + r - 1 ] +% Author: Nicole Stock +% Date: Fall 2020 u_vec_r = @(r,z) (1./2).*r.*z - (1./2).*r.*z.^2; u_vec_th = @(r,z) 0;