Hi Safdar,
The Poisson equation using finite element method for P2 can be solved using the “solvepde” function in MATLAB.
You can refer to the code below to solve the Poisson equation for P2:
model = createpde();
% Define the Geometry (Unit Square)
R1 = [3,4,0,1,1,0,0,0,1,1]';
gd = [R1];
ns = char('R1');
ns = ns';
sf = 'R1';
g = decsg(gd,sf,ns);
geometryFromEdges(model, g);
generateMesh(model, 'Hmax', 0.1, 'GeometricOrder', 'quadratic');
% Specify PDE Coefficients for Poisson's Equation
% -∇·(∇u) = f, where c = 1, a = 0, f = 1
specifyCoefficients(model, 'm', 0, 'd', 0, 'c', 1, 'a', 0, 'f', 1);
applyBoundaryCondition(model, 'dirichlet', 'Edge', 1:model.Geometry.NumEdges, 'u', 0);
% Solve the PDE
result = solvepde(model);
u = result.NodalSolution;
pdeplot(model, 'XYData', u, 'ZData', u, 'Mesh', 'on');
title('Solution of Poisson Equation on a Unit Square');
xlabel('x');
ylabel('y');
zlabel('u(x,y)');
Refer to this link for more information on “solvepde”: https://www.mathworks.com/help/pde/ug/pde.pdemodel.solvepde.html
Hope this helps!!
