Interpolation Error-Based *A Posteriori *Error Estimation
for P-Refinement

Using First and Second Derivative Jumps

*Hp*-adaptive finite element methods require estimates of the error
in the solution at the current order and one order higher. Interpolation-error
based *a posteriori *error estimates offer one solution to this problem.
I show how such estimates at the current order can be obtained in one dimension
for odd (even) order bases by using jumps in the first (second) derivative
of the finite element solution at element boundaries. Additionally
the jumps in the second (first) derivative for odd (even) order elements
allow error estimates of the finite element solution one order higher than
the current order to be computed. These estimates are compared with
interpolation-error based methods that use high-order derivative approximations
of the finite element solution. Computational results illustrate the theory
and the impact of the estimation strategy on the refinement algorithm is
discussed.