Blar i Fakultet for informasjonsteknologi og elektroteknikk (IE) på tidsskrift "SIAM Journal on Numerical Analysis"
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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 ... -
On the rate of convergence for monotone numerical schemes for nonlocal Isaacs equations
(Journal article; Peer reviewed, 2019)We study monotone numerical schemes for nonlocal Isaacs equations, the dynamic programming equations of stochastic differential games with jump-diffusion state processes. These equations are fully nonlinear nonconvex ... -
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory
(Journal article; Peer reviewed, 2019)We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $\partial_t u-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=f \;\text{in}\; \mathbb{R}^ ... -
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments
(Journal article; Peer reviewed, 2018)We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $\partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t)$ in $\mathbb{R}^N\times(0,T),$ where ...