We consider the Dirichlet problem for elliptic systems with periodically distributed inclusions with significant contrast compared to the background media.
A unified method is developed to quantify convergence rates as the periodicity of inclusions tends to zero and as the parameter approaches either zero or infinity.
Based on the obtained convergence rates and a Campanato-type scheme, regularity estimates that are uniform in both periodicity and contrast are derived.
The spectral difference method based on p-th order Raviart - Thomas space is studied for the scalar transport equation on regular triangular meshes.