Mimicking of Non-conservative Systems: Demonstration of a generalized method for applying the mimetic spectral element method to non-conservative systems

The mimetic spectral element method is a relatively young method in numerical solutions of partial differential equations and actions that describe physical systems. Its advantage is that it takes the geometrical structure of the problem into account which guarantees consistency of the numerical scheme and the conservation of relevant quantities...

Analysis of Laplace eigenvalues using Spectral element methods

In order to solve a partial differential equation numerically it has to be replaced with a system of equations. The methods which can preserve these essential mathematical and physical structures are called mimetic methods.<br/><br/>The equation that we focus in this thesis is Laplace operator. Differential forms are used to describe the Laplace...

Structure Preserving Isogeometric Analysis for Computational Fluid Dynamics

Double degree. Supervision of the thesis also at: Faculty Applied Mathematics, Department Numerical Analysis, Programme M.Sc. Applied Mathematics. Structure-preserving discretization techniques preserve fundamental structure of operators and operands found in partial differential equations. Classical discretization techniques sometimes neglect...

An Application of Discrete Differential Geometry to the Spectral Element Method

The thesis describes how differential geometry and algebraic topology together can be applied to an existing numerical method. After some introduction, the central idea is explained, after which a chapter is devoted to error approximation of the method. Finally, a 1D application is completely written out and the results are analysed.