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Implementing finite elements in Mma ?

I try to test some simple (one-dimensional) finite-element algorithms in
Mathematica, and havn't found yet a way to program them in a way to keep
them symbolically integratable. The function below calculates the value of
the i-th linear finite element phi_i at time t based on the array of
timevalues that defines where the respective finite elements should be 1
or 0 (phi_i(t_j) = delta_ij (kronecker)). But the way its implemented only
allows for numerical integration. Any idea?

Thanks, Christian.

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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