Blar i NTNU Open på forfatter "Solem, Susanne"
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Convergence and convergence rates of numerical methods for conservation laws
Solem, Susanne (Doctoral theses at NTNU;2019:11, Doctoral thesis, 2019) -
Convergence Rates of the Front Tracking Method for Conservation Laws in the Wasserstein Distances
Solem, Susanne (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 ... -
A Convergent Numerical Algorithm for α-Dissipative Solutions of the Hunter–Saxton Equation
Christiansen, Thomas; Grunert, Katrin; Nordli, Anders Samuelsen; Solem, Susanne (Peer reviewed; Journal article, 2024)A convergent numerical method for -dissipative solutions of the Hunter–Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initial data, and then solving exactly using the ... -
Noise-driven bifurcations in a neural field system modelling networks of grid cells
Carrillo, José A.; Holden, Helge; Solem, Susanne (Peer reviewed; Journal article, 2022)The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns ... -
Numerical conservative solutions of the Hunter–-Saxton equation
Grunert, Katrin; Nordli, Anders Samuelsen; Solem, Susanne (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
Erhardt, André Henrik; Solem, Susanne (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
Solem, Susanne (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
Solem, Susanne; Fjordholm, Ulrik Skre; Carrillo, José A (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
Ruf, Adrian Montgomery; Sande, Espen; Solem, Susanne (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 ... -
Traveling Wave Solutions for the Hunter-Saxton Equation
Christiansen, Thomas (Master thesis, 2021)I denne oppgaven studerer vi vandrende bølgeløsninger for Hunter-Saxton likningen. Vi benytter en lime-formalisme som lar oss lime sammen to klassiske vandrende løsninger langs en kurve. Dette lar oss konstruere svake ...