Explicit Flux Balancing Domain Decomposition for Spectral Collocations: Basics and 1D Applications

A non-overlapping multidomain spectral collocation method for partial differential equations is developed. Using domain partitioning, geometrical flexibility and decrease in computational cost within global spectral approximation is achieved by an explicit flux balancing at sub-domain interfaces. While retaining high-order accuracy and simplicity, it is shown that this interface condition allows steep gradients in the solution near regions with discountinuties like shocks without any post-processing or filtering.