Davide Fassino
New results on the a posteriori error analysis for Virtual Element Methods.
Rel. Claudio Canuto. Politecnico di Torino, Corso di laurea magistrale in Ingegneria Matematica, 2022
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Abstract
In order to describe the world and its phenomena, an essential concept is necessary: the derivative. Derivative is the mathematical way to describe the evolution in time or in space. By combining derivatives and some constraints observed, which are described as equations, the partial differential equations (PDE) arise. Most of the time we can just discuss some properties of the solution of a PDE, but finding the explicit solution can be analytically impossible. Numerical Analysis tries to solve this problem with the Finite Element Method (FEM). This method is based on finding an approximation of the real solution; it gets more precise as the degree of accuracy grows.
FEM considers a discretization of the domain made by finite elements, defined by a triple which consists in the ‘geometrical shape’ E of the element forming the partition, a space of approximation functions living in E and a set of degrees of freedom
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