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Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements

Grohs, Philipp ; Hardering, Hanne ; Sander, Oliver

In: Foundations of Computational Mathematics, 2015, vol. 15, no. 6, p. 1357-1411

Maximal metric surfaces and the Sobolev-to-Lipschitz property

Creutz, Paul ; Soultanis, Elefterios

In: Calculus of Variations and Partial Differential Equations, 2020, vol. 59, no. 5, p. 177

We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spaces and obtain a variant of the associated intrinsic disc studied by...

Adaptive wavelet methods for elliptic partial differential equations with random operators

Gittelson, Claude

In: Numerische Mathematik, 2014, vol. 126, no. 3, p. 471-513

Regularity of quasi-n-harmonic mappings into NPC spaces

Guo, Chang-Yu ; Xiang, Chang-Lin

In: Annali di Matematica Pura ed Applicata (1923 -), 2019, vol. 198, no. 2, p. 367–380

We prove local Hölder continuity of quasi-n-harmonic mappings from Euclidean domains into metric spaces with non-positive curvature in the sense of Alexandrov. We also obtain global Hölder continuity of such mappings from bounded Lipschitz domains.

Stable multilevel splittings of boundary edge element spaces

Hiptmair, Ralf ; Mao, Shipeng

In: BIT Numerical Mathematics, 2012, vol. 52, no. 3, p. 661-685

Non-Reflecting Boundary Conditions for Maxwell's Equations

Hiptmair, R. ; Schädle, A.

In: Computing, 2003, vol. 71, no. 3, p. 265-292

Sparse tensor edge elements

Hiptmair, Ralf ; Jerez-Hanckes, Carlos ; Schwab, Christoph

In: BIT Numerical Mathematics, 2013, vol. 53, no. 4, p. 925-939

Optimization problems for weighted Sobolev constants

Bandle, Catherine ; Wagner, Alfred

In: Calculus of Variations and Partial Differential Equations, 2007, vol. 29, no. 4, p. 481-507

General DG-Methods for Highly Indefinite Helmholtz Problems

Melenk, J. ; Parsania, A. ; Sauter, S.

In: Journal of Scientific Computing, 2013, vol. 57, no. 3, p. 536-581

Convergence analysis of finite element methods for H (curl; Ω)-elliptic interface problems

Hiptmair, Ralf ; Li, Jingzhi ; Zou, Jun

In: Numerische Mathematik, 2012, vol. 122, no. 3, p. 557-578