60 citations · 102 across the 14 of their papers we have counts for
18 papers
Data-dependent density estimation for the Fokker-Planck equation in higher dimensions
Max Jensen, Fabian Merle, Andreas Prohl
We present a new strategy to approximate the global solution of the Fokker-Planck equation efficiently in higher dimensions and show its convergence. The main ingredients are the E…
Deep learning for gradient flows using the Brezis-Ekeland principle
Laura Carini, Max Jensen, Robert Nürnberg
We propose a deep learning method for the numerical solution of partial differential equations that arise as gradient flows. The method relies on the Brezis--Ekeland principle, whi…
Finite Element Approximation of Hamilton-Jacobi-Bellman equations with nonlinear mixed boundary conditions
Bartosz Jaroszkowski, Max Jensen
We show strong uniform convergence of monotone P1 finite element methods to the viscosity solution of isotropic parabolic Hamilton-Jacobi-Bellman equations with mixed boundary cond…
Finite Element Methods for Isotropic Isaacs Equations with Viscosity and Strong Dirichlet Boundary Conditions
Bartosz Jaroszkowski, Max Jensen
We study monotone P1 finite element methods on unstructured meshes for fully non-linear, degenerately parabolic Isaacs equations with isotropic diffusions arising from stochastic g…
Dynamic Programming for Finite Ensembles of Nanomagnetic Particles
Max Jensen, Ananta Majee, Andreas Prohl +1
We use optimal control via a distributed exterior field to steer the dynamics of an ensemble of N interacting ferromagnetic particles which are immersed into a heat bath by minimiz…
Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions
Max Jensen, Axel Målqvist, Anna Persson
We prove strong convergence for a large class of finite element methods for the time-dependent Joule heating problem in three spatial dimensions with mixed boundary conditions on L…
Numerical Solution of the Simple Monge-Ampère Equation with Non-convex Dirichlet Data on Non-convex Domains
Max Jensen
The existence of a unique numerical solution of the semi-Lagrangian method for the simple Monge-Ampère equation is known independently of the convexity of the domain or Dirichlet b…
On the notion of boundary conditions in comparison principles for viscosity solutions
Max Jensen, Iain Smears
We collect examples of boundary-value problems of Dirichlet and Dirichlet-Neumann type which we found instructive when designing and analysing numerical methods for fully nonlinear…
Convergent semi-Lagrangian methods for the Monge-Ampère equation on unstructured grids
Xiaobing Feng, Max Jensen
This paper is concerned with developing and analyzing convergent semi-Lagrangian methods for the fully nonlinear elliptic Monge-Ampère equation on general triangular grids. This is…
Finite Element Convergence for Degenerate Isotropic Hamilton-Jacobi-Bellman Equations
Max Jensen
In this paper we study the convergence of monotone finite element methods for fully nonlinear Hamilton-Jacobi-Bellman equations with degenerate, isotropic diffusions. The main…
On the Stability of Continuous-Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems
Andrea Cangiani, John Chapman, Emmanuil Georgoulis +1
We consider a finite element method which couples the continuous Galerkin method away from internal and boundary layers with a discontinuous Galerkin method in the vicinity of laye…
Discontinuous Galerkin Methods for Mass Transfer through Semi-Permeable Membranes
Andrea Cangiani, Emmanuil H. Georgoulis, Max Jensen
A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multi-compartment partial differential equation (PDE) models, interconnected with interfac…
On Local Super-Penalization of Interior Penalty Discontinuous Galerkin Methods
Andrea Cangiani, John Chapman, Emmanuil H. Georgoulis +1
We prove in an abstract setting that standard (continuous) Galerkin finite element approximations are the limit of interior penalty discontinuous Galerkin approximations as the pen…
Finite Element Convergence for the Joule Heating Problem with Mixed Boundary Conditions
Max Jensen, Axel Målqvist
We prove strong convergence of conforming finite element approximations to the stationary Joule heating problem with mixed boundary conditions on Lipschitz domains in three spatial…
Implementation of the Continuous-Discontinuous Galerkin Finite Element Method
Andrea Cangiani, John Chapman, Emmanuil Georgoulis +1
For the stationary advection-diffusion problem the standard continuous Galerkin method is unstable without some additional control on the mesh or method. The interior penalty disco…
Finite Element Methods with Artificial Diffusion for Hamilton-Jacobi-Bellman Equations
Max Jensen, Iain Smears
In this short note we investigate the numerical performance of the method of artificial diffusion for second-order fully nonlinear Hamilton-Jacobi-Bellman equations. The method was…
On the Convergence of Finite Element Methods for Hamilton-Jacobi-Bellman Equations
Max Jensen, Iain Smears
In this note we study the convergence of monotone P1 finite element methods on unstructured meshes for fully non-linear Hamilton-Jacobi-Bellman equations arising from stochastic op…
Stable Crank-Nicolson Discretisation for Incompressible Miscible Displacement Problems of Low Regularity
Max Jensen, Ruediger Mueller
In this article we study the numerical approximation of incompressible miscible displacement problems with a linearised Crank-Nicolson time discretisation, combined with a mixed fi…