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(Solved): T3 finite element is defined over triangle ABC (in physical coordinates). The vertices of this trian ...
T3 finite element is defined over triangle ABC (in physical coordinates). The vertices of this triangle have
the following coordinates: A(5,-7),B(-3,8), and C(-6,-5).
Problem 1.
Calculate the partial derivatives of T3 basis functions with respect to the physical coordinates x
and y.
Problem 2.
a\int_(\Delta ABC) f(x,y)dS
where f(x,y)=5x^(2)-3y^(2)+6x-y.
bf(x,y)=cos(\pi x)-sin(y) is going to be represented by T3 basis functions over
triangle ABC. Calculate the values of the degrees of freedom C_(i) in the linear combination that
represents f(x,y) at the vertices of the triangle ABC :
f(x,y)=\sum_(i=1)^m C_(i)N_(i)(x,y)
Note: please use radians when evaluate the trigonometric functions.