Now showing items 1-7 of 7

• #### Convergence and convergence rates of numerical methods for conservation laws ﻿

(Doctoral theses at NTNU;2019:11, Doctoral thesis, 2019)
• #### Convergence Rates of the Front Tracking Method for Conservation Laws in the Wasserstein Distances ﻿

(Journal article; Peer reviewed, 2018)
We prove that front tracking approximations to scalar conservation laws with convex fluxes converge at a rate of $\Delta x^2$ in the 1-Wasserstein distance $W_1$. Assuming positive initial data, we also show that the ...
• #### Numerical conservative solutions of the Hunter–-Saxton equation ﻿

(Peer reviewed; Journal article, 2021)
In the article a convergent numerical method for conservative solutions of the Hunter–Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the ...
• #### On complex dynamics in a Purkinje and a ventricular cardiac cell model ﻿

(Journal article; Peer reviewed, 2021)
Cardiac muscle cells can exhibit complex patterns including irregular behaviour such as chaos or (chaotic) early afterdepolarisations (EADs), which can lead to sudden cardiac death. Suitable mathematical models and their ...
• #### Relaxation Systems with Applications to Two-Phase Flow ﻿

(Master thesis, 2014)
Relaxation systems are widely studied and much used to describe nonequilibrium phenomena, occurring in, for example, two-phase flow. In this thesis we will therefore consider relaxation systems in one space dimension and ...
• #### A second-order numerical method for the aggregation equations ﻿

(Peer reviewed; Journal article, 2020)
Abstract: Inspired by so-called TVD limiter-based second-order schemes for hyperbolic conservation laws, we develop a formally second-order accurate numerical method for multi-dimensional aggregation equations. The method ...
• #### The Optimal Convergence Rate of Monotone Schemes for Conservation Laws in the Wasserstein Distance ﻿

(Journal article; Peer reviewed, 2019)
In 1994, Nessyahu, Tadmor and Tassa studied convergence rates of monotone finite volume approximations of conservation laws. For compactly supported, Lip+ -bounded initial data they showed a first-order convergence rate ...