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Implementing finite element basis functions in Mma

I try to test out a finite element algorithm in Mathematica, where the
basis functions phi_i for a given vector of numbers {x1,x2,...xn} with
x1<x2<..<xn are piecewise linear and phi_i(xj) = delta(i,j) (kronecker
The function below returns the value of the i-th basis function at number
t, but the way I implemented it makes symbolic integration (for example
the integral of phi_i * phi_j or D[phi_i,x]*phi_j) impossible. Any ideas
how I have to write the basis functions to maintain the symbolic calculus?

Thanks for your interest, Christian.

ps: sorry if you have read this before, but our server had some problems
so I could not verify if the original post made it to the net.

numberQ[x_] := NumberQ[N[x]]

BasisFunctions[i_Integer, t_Real,timeValue:{_?numberQ..}] :=
         len = Length[timeValue];
     If[Length[(sublist= Position[(# < t)& /@timeValue,False])] > 0,
      posOfT = sublist[[1,1]];, posOfT = 0;];
      Which[t<timeValue[[1]], (* beginning of which*)
         value = 0.0,
         posOfT == i,
         posOfT == i+1,
         0.0 ] (* end of which *)

Christian Jost, Université Paris-Sud XI, Orsay, France

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