The course provides at an entry graduate level the theory and practice of finite difference and finite elements methods for partial differential equations (PDEs) encountered in fluid dynamics and solid mechanics. Topics covered include: classification of partial PDEs and characteristics; direct and iterative solution methods for solution of algebraic systems; finite difference and finite element spatial discretization; temporal discretization; consistency, stability and error analysis; explicit and implicit finite differencing and finite element schemes for linear hyperbolic, parabolic, elliptic PDEs. The course requires completion of several projects using MATLAB. Students cannot receive credit for this course if they have taken AE/ME 5108 “Computational Fluid Dynamics”.
AE 5031: Applied Computational Methods for Partial Differential Equations
Department