The Nitsche method is a method of “weak imposition” of the Dirichlet boundary conditions for partial differential equations. The stability and error estimate of Nitsche’s method for evolutionary diffusion-advection-reaction equations are studied by the variational method, which is popular method for studying the elliptic problems. The inf-sup condition and Galerkin orthogonality give the optimal order error estimate in some appropriate norms under regularity assumptions on the exact solution.

Dr. Yuki Ueda obtained his Ph.D. degree in 2018 at The University of Tokyo. Then, He worked as a project researcher at The University of Tokyo. In 2019, Dr. Ueda joined The Hong Kong Polytechnic University as a postdoc. His research focuses on the numerical analysis for PDEs, especially FEM and application of NURBS basis functions.