Electrokinetic transport phenomena in complex fluids and multiphysics systems present formidable computational challenges due to strong nonlinearities, multiscale dynamics, and coupled physical processes, which conventional methods fail to resolve efficiently. This study introduces a robust high-order adaptive numerical scheme that integrates spectral accuracy, dynamic adaptability, and computational efficiency to address these limitations. The framework combines Fourier-based spectral discretization with hp-adaptive mesh refinement to resolve sharp gradients and evolving interfaces, a stabilized pseudo-spectral approach for nonlinear terms (e.g., ion transport, Joule heating), and an Implicit-Explicit (IMEX) time-stepping strategy to handle stiffness. A novel a posteriori error estimator guides spatiotemporal adaptation, optimizing resource use without sacrificing precision. Validation demonstrates spectral convergence (errors decaying as O(10^(-9) )) and a 50% reduction in computational cost compared to finite element methods for electro-osmotic flow. Large-scale 3D simulations of heterogeneous microfluidic systems further showcase the scheme’s ability to resolve multiphysics couplings (electrohydrodynamics, thermal effects) with high fidelity. By unifying high-order accuracy, nonlinear stability, and adaptive efficiency, this work advances predictive modeling for electrokinetic-driven technologies in microfluidics, bioMEMS, and energy conversion systems.