Resolving Boundary Layers with Harmonic Extension Finite Elements

In recent years, the standard numerical methods for partial differential equations have been extended with variants that address issue of domain discretisation in complicated domains. Sometimes similar requirements are induced by local parameter-dependent features solutions, instance, boundary or internal layers. The adaptive reference elements one way which harmonic extension elements, an p-version finite element method, can be implemented. combination simple replacement rule-based mesh generation, performance method is shown to equivalent problems where layers dominate solution. over a parameter range demonstrated application computational asymptotic analysis, known estimates recovered via means only.