Applied Mathematics / Finite element method / Finite Element / Higher Order Thinking / Parabolic Wave Equation / Adaptive Mesh Refinement / Time Dependent / Numerical Analysis and Computational Mathematics / Point of View / Finite Element Approximation / Direct Method / Exact solution methods / Order of Convergence / Adaptive Mesh Refinement / Time Dependent / Numerical Analysis and Computational Mathematics / Point of View / Finite Element Approximation / Direct Method / Exact solution methods / Order of Convergence