A C0 interior penalty method for 4th order PDE's
Fourth order Partial Differential Equations (PDE's) arise in many different physic's fields. As an example, the research group for Mathematical and Computational Modeling at UPC LaCàN is studying flexoelectricity, a very promising field which aims to replace some of the uses of piezoelectr...
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| Formato: | tesis de maestría |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/166048 |
| Acesso em linha: | https://hdl.handle.net/2117/166048 |
| Access Level: | acceso abierto |
| Palavra-chave: | Difference equations, Partial--Numerical solutions PDE FEM 4th order IPM Nitsche Flexoelectricity Kirchoff plate Equacions diferencials parcials--solucions numèriques Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
| Resumo: | Fourth order Partial Differential Equations (PDE's) arise in many different physic's fields. As an example, the research group for Mathematical and Computational Modeling at UPC LaCàN is studying flexoelectricity, a very promising field which aims to replace some of the uses of piezoelectric materials, and whose equations involve 4th order derivatives. This work provides a method to solve these 4th order PDE's using the Finite Element Method (FEM) with C0 elements, which provides many advantages with respect to other methods that involve using C1 elements or decoupling the equation. The method is developed over the equations of the deformation of a Kirchoff plate, which is also a 4th order PDE. This method is then successfully validated with numerical experiments, both physical and artificial. An analysis of the convergence as well as the method's sensitivity to a newly added parameter is also provided. Due to the success of the method, LaCàN group will use this method to solve flexoelectricity's PDE's. |
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