weak_prob2.m

drlt 边界限元程序

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% Singular (3-x)ln(2-x) Gauss integration for 3 Gauss points on[0,2]%
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clear



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% n = 3


% regular on [-1,1]
eta=[-sqrt(0.6) 0 sqrt(0.6)];
weights = [5/9  8/9  5/9];

% singular on [0,1]
weights_sing=[0.51340455 0.39198004 0.09461541];
eta_sing=[0.06389079 0.36899706 0.76688030];


%singular integral
I_sing = 0;
for i=1:3
    I_sing=I_sing - (4 * eta_sing(i) + 2) * weights_sing(i)
end


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% regular integral --> Use structure from homework three and define 
%function in f_prob2 
a=0;
b=1;
% Gauss points on [a,b]
x3 = (a+b)*0.5 + (b-a)*0.5*eta;

jacobian=(b-a)/2;


% Coordinate Transform on [a,b]
I_reg= jacobian * weights * f_prob2(x3)'


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I = I_sing + I_reg
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%Plot function

x=(0:0.001:2);
y=(3-x).*log(2-x);
figure(2)
plot(x,y,'Linewidth',2)
xlabel('x','FontSize',16)
ylabel('f(x)','FontSize',16)
title([' Problem 2: f(x)'],'Fontsize',16)
%axis([0 2 0 .5])
grid on;