  The Reduced Basis (RB) method is a well established method for the model
order reduction of problems formulated as parametrized partial differential
equations. One crucial requirement for the application of RB schemes is the
availability of an a posteriori error estimator to reliably estimate the error
introduced by the reduction process. However, straightforward implementations
of standard residual based estimators show poor numerical stability, rendering
them unusable if high accuracy is required. In this work we propose a new
algorithm based on representing the residual with respect to a dedicated
orthonormal basis, which is both easy to implement and requires little
additional computational overhead. A numerical example is given to demonstrate
the performance of the proposed algorithm.
