Adaptive collocation methods for the solution of partial differential equations

• Author(s): Brito, Paulo ; Portugal, António
• Date: 2010
• Persistent ID: http://hdl.handle.net/10198/4042
• Origin: Biblioteca Digital do IPB
• Subject(s): Partial differential equation; Numerical methods; Adaptive methods; Collocation methods; Dyadic grids
• Document Type: Article
• Language: English

Description

An integration algorithm that conjugates a Method of Lines (MOL) strategy based on finite differences space discretizations, with a collocation strategy based on increasing level dyadic grids is presented. It reveals potential either as a grid generation procedure and a Partial Differential Equation(PDE) integration scheme. It copes satisfactorily with a example characterized by a steep travelling wave and a example that presented a forming steep shock, which demonstrates its versatility in dealing with different types of steep moving front problems, exhibiting features like advection-diffusion, widely common in the standard Chemical Processes simulation models.