Optimal a priori discretization error bounds for geodesic finite elements
From MaRDI portal
Publication:895697
DOI10.1007/s10208-014-9230-zzbMath1331.65153OpenAlexW2129261057MaRDI QIDQ895697
Hanne Hardering, Philipp Grohs, Oliver Sander
Publication date: 4 December 2015
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: http://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-010586%22
Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
Related Items
\(\varepsilon\)-subgradient algorithms for locally Lipschitz functions on Riemannian manifolds, A second-order TV-type approach for inpainting and denoising higher dimensional combined cyclic and vector space data, Mumford-Shah and Potts regularization for manifold-valued data, Numerical treatment of a geometrically nonlinear planar Cosserat shell model, \(L^{2}\)-discretization error bounds for maps into Riemannian manifolds, Geometry of logarithmic strain measures in solid mechanics, Interpolation on symmetric spaces via the generalized polar decomposition, On Multiscale Quasi-Interpolation of Scattered Scalar- and Manifold-Valued Functions, A geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: discretization with geometric finite elements, Wavelet Sparse Regularization for Manifold-Valued Data, A posteriori error estimates for wave maps into spheres, Quasi-Optimal Error Estimates for the Finite Element Approximation of Stable Harmonic Maps with Nodal Constraints, Embedding-Based Interpolation on the Special Orthogonal Group, Projection-Based Finite Elements for Nonlinear Function Spaces, Geometric Finite Elements, Geometric Subdivision and Multiscale Transforms, High-Order Retractions on Matrix Manifolds Using Projected Polynomials, Scattered manifold-valued data approximation, Convergence of subdivision schemes on Riemannian manifolds with nonpositive sectional curvature, A Second Order Nonsmooth Variational Model for Restoring Manifold-Valued Images, Total Generalized Variation for Manifold-Valued Data, Variational discretizations of gauge field theories using group-equivariant interpolation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Transversely isotropic material: nonlinear Cosserat versus classical approach
- A finite-strain elastic-plastic Cosserat theory for polycrystals with grain rotations
- On a stress resultant geometrically exact shell model. I: Formulation and optimal parametrization
- Interpolatory wavelets for manifold-valued data
- The imbedding problem for Riemannian manifolds
- Smoothness equivalence properties of univariate subdivision schemes and their projection analogues
- Riemannian geometry for the statistical analysis of diffusion tensor data
- Approximation order from stability for nonlinear subdivision schemes
- Theory and FE analysis for structures with large deformation under magnetic loading
- A regularity theory for harmonic maps
- A three-dimensional finite-strain rod model. II. Computational aspects
- Existence and partial regularity of static liquid crystal configurations
- Uniqueness and stability of harmonic maps and their Jacobi fields
- Everywhere discontinuous harmonic maps into spheres
- Geometry of \(F\)-harmonic maps
- On a stress resultant geometrically exact shell model. III: Computational aspects of the nonlinear theory
- Orthonormal vector sets regularization with PDE's and applications
- Topology of Sobolev mappings. II.
- Sobolev spaces and harmonic maps for metric space targets
- Approximation variationnelle des problèmes aux limites
- Geometric multiscale decompositions of dynamic low-rank matrices
- Geometry of manifolds of maps
- A Riemannian framework for tensor computing
- Approximation order of interpolatory nonlinear subdivision schemes
- Geodesic Finite Elements in Spaces of Zero Curvature
- Quasi-interpolation in Riemannian manifolds
- Interpolatory Multiscale Representation for Functions between Manifolds
- Approximation order equivalence properties of manifold-valued data subdivision schemes
- Simulation of Q-Tensor Fields with Constant Orientational Order Parameter in the Theory of Uniaxial Nematic Liquid Crystals
- Geodesic finite elements on simplicial grids
- A General Proximity Analysis of Nonlinear Subdivision Schemes
- An Online Method for Interpolating Linear Parametric Reduced-Order Models
- Numerical analysis of a finite element scheme for the approximation of harmonic maps into surfaces
- Geodesic finite elements for Cosserat rods
- Constraint preserving implicit finite element discretization of harmonic map flow into spheres
- Sobolev Mappings between Manifolds and Metric Spaces
- A geometrically exact thin membrane model—investigation of large deformations and wrinkling
- Riemannian center of mass and mollifier smoothing
- A Report on Harmonic Maps
- Thin shells with finite rotations formulated in biot stresses: Theory and finite element formulation
- Relaxation Methods for Liquid Crystal Problems
- Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
- A New Algorithm For Computing Liquid Crystal Stable Configurations: The Harmonic Mapping Case
- Color image enhancement via chromaticity diffusion
- Symplectic Rotational Geometry in Human Biomechanics
- Means and Averaging in the Group of Rotations
- The interplay between analysis and topology in some nonlinear PDE problems
- A GEOMETRICALLY EXACT PLANAR COSSERAT SHELL-MODEL WITH MICROSTRUCTURE: EXISTENCE OF MINIMIZERS FOR ZERO COSSERAT COUPLE MODULUS
- Multiscale Representations for Manifold-Valued Data
- Stability and Convergence of Finite-Element Approximation Schemes for Harmonic Maps
- Harmonic Mappings of Riemannian Manifolds
- Riemannian geometry and geometric analysis
- Harmonic maps with potential
