It is created by dividing a domain into a set of quadrilaterals that have unequal sides. Here is an example of how to create a Bakhvalov mesh in MATLAB:

Define the domain and number of elements:

Lx = 1; % length of domain in x-direction

Ly = 1; % length of domain in y-direction

ne = 10; % number of elements in each direction

Define the spacing between the nodes in the x and y directions:

dx = Lx/ne; % spacing between nodes in x-direction

dy = Ly/ne; % spacing between nodes in y-direction

Create the mesh:

x = linspace(0,Lx,ne+1); % x-coordinates of nodes

y = linspace(0,Ly,ne+1); % y-coordinates of nodes

[X,Y] = meshgrid(x,y); % create a meshgrid of nodes

% create the connectivity matrix for the elements

conn = zeros(ne^2,4);

for i = 1:ne

for j = 1:ne

n1 = (ne+1)*(i-1) + j;

n2 = (ne+1)*i + j;

n3 = (ne+1)*i + j+1;

n4 = (ne+1)*(i-1) + j+1;

elem = (i-1)*ne + j;

conn(elem,:) = [n1 n2 n3 n4];

end

end

Plot the mesh:

figure;

patch('Faces',conn,'Vertices',[X(:) Y(:)],'FaceColor','none','EdgeColor','k');

xlabel('x');

ylabel('y');