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Session S20 - Applied Math and Computational Methods and Analysis across the Americas

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Approximation of non-homogeneous partial differential equations using the Scaled Boundary Finite Element Method

Karolinne O. Coelho

State University of Campinas, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The Scaled Boundary Finite Element Method (SBFEM) is a semi-analytical technique in which finite element spaces are constructed based on the approximation of local Dirichlet problems with piecewise polynomial trace data. The basis functions are Duffy's approximations with a gradient-orthogonality constraint imposed to solve homogeneous partial differential equations (PDEs) - a mimetic version of harmonic functions. Since the method was originally proposed for homogeneous PDEs, loss of convergence is observed in formulations where a source term is present. Therefore, this study aims to develop a formulation to approximate non-homogeneous partial differential equations based on orthogonal bubble functions. Due to the orthogonality property, the approximation of non-homogeneous PDE using the SBFEM can be decoupled into boundary and domain problems and be solved separately. Three examples show the accuracy and optimal rates of convergence for a parabolic PDE (a heat flow) and Elasticity problems.

Joint work with Philippe R. B. Devloo (University of Campinas).

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