arXiv subjects

Nils Bullerjahn

Publications and source records attributed to Nils Bullerjahn.

3 recordsLinked to original sources

arXiv2026

Error estimates for $A$-stable backward difference full discretizations of Willmore flow of closed surfaces

A proof of optimal-order $H^1$-norm error estimates is given for $A$-stable backward difference full discretizations (of order 1 and 2) of Willmore flow for closed two-dimensional surfaces. The numerical method discretizes a coupled system of evolution equations by evolving surface finite elements of polynomial degree at least two in space and backward difference method of order 1 or 2 in time. The convergence analysis is based on a stability analysis, based on energy estimates exploiting the anti-symmetric structure of the second-order system, in combination with Dahlquist's $G$-stability and the multiplier techniques of Nevanlinna and Odeh, with a new upper bound in the spirit of Dahlquist. Numerical experiments illustrate and complement the theoretical results.

math.NA↗

arXiv2026

Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions

A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order one to five in time. The error estimates are obtained by a consistency and stability analysis, based on an energy estimate and the novel approach of exploiting the almost mass conservation of the error equations to derive a Poincaré-type inequality. We demonstrate how this approach can be generalized to other almost mass conserving problems. To this end we prove optimal-order fully discrete error estimates for the Cahn--Hilliard equation on evolving surfaces. We illustrate and complement our findings by numerical experiments.

math.NA↗

arXiv2025

Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions

A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order 1 to 5 in time. Optimal-order error estimates are proven. The error estimates are based on a consistency and stability analysis in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system.

math.NA↗