Ada J. Ellingsrud

TL;DR: This paper introduces and numerically evaluates a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree and studies ephaptic coupling induced in an unmyelinated axon bundle.

TL;DR: This paper introduces high level mathematical software abstractions together with lower level algorithms for expressing and efficiently solving mixed dimensional PDEs of co-dimension up to one (i.e. nD-mD with |n-m| <= 1).

TL;DR: In this article, a homogenized model for ionic electrodiffusion and osmosis in brain tissue is considered and different finite element-based splitting schemes are evaluated in terms of their numerical properties, including accuracy, convergence and computational efficiency for both idealized scenarios and for the physiologically relevant setting of cortical spreading depression (CSD).

TL;DR: This paper introduces and numerically evaluates a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree and studies ephaptic coupling induced in an unmyelinated axon bundle.

TL;DR: In this paper, the authors present general abstractions and algorithms for finite element discretizations of mixed domain and mixed dimensional PDEs of codimension up to one (i.e., nD-mD with |n-m| ≤ 1).