We present work towards the development of reliable and automated computational tools for partial differential equations (PDEs) in continuum mechanics with an emphasis on aerodynamics. The talk covers two topics: adaptive high-order method and model reduction for parametrized PDEs. Adaptive high-order method addresses classical engineering scenarios that require high-fidelity analysis of one or few configurations. Our approach builds on a high-order discontinuous Galerkin method, output error estimate, and anisotropic adaptive mesh refinement. We demonstrate efficient and automatic discretization error control for aerodynamic flows. Model reduction addresses many-query and real-time scenarios that require rapid analysis for thousands of different configurations. We present our work to provide rigorous error bounds, treat nonlinear equations that exhibit limited stability, and incorporate model reduction training information across different cases. We demonstrate the use of model reduction to enable combined discretization and model uncertainty quantification (UQ) for aerodynamic flows with control on finite element, model reduction, and statistical sampling errors.