OOIR: Observatory of International Research

Papers

(The median citation count of Numerische Mathematik is 2. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2021-02-01 to 2025-02-01.)

Article	Citations
Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation	22
On the spectrum of the double-layer operator on locally-dilation-invariant Lipschitz domains	20
A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions	20
Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates	19
A model reduction approach for inverse problems with operator valued data	19
New analysis and recovery technique of mixed FEMs for compressible miscible displacement in porous media	19
Large-stepsize integrators for charged-particle dynamics over multiple time scales	18
Minimum-correction second-moment matching: theory, algorithms and applications	17
A proximal-gradient algorithm for crystal surface evolution	15
Convergent adaptive hybrid higher-order schemes for convex minimization	14
Kernel-independent adaptive construction of $$\mathcal {H}^2$$-matrix approximations	13
Improved error estimates for the finite volume and the MAC schemes for the compressible Navier–Stokes system	12
New discontinuous Galerkin algorithms and analysis for linear elasticity with symmetric stress tensor	12
Preconditioning high order $$H^2$$ conforming finite elements on triangles	11
Which constraints of a numerical problem cause ill-conditioning?	11
Functions of rational Krylov space matrices and their decay properties	10
A convergent finite volume scheme for dissipation driven models with volume filling constraint	10
Fully discrete loosely coupled Robin-Robin scheme for incompressible fluid–structure interaction: stability and error analysis	10
Corners and stable optimized domain decomposition methods for the Helmholtz problem	10
Projection in negative norms and the regularization of rough linear functionals	9
Nearest $$\varOmega $$-stable matrix via Riemannian optimization	9
Drift approximation by the modified Boris algorithm of charged-particle dynamics in toroidal geometry	9
Improved ParaDiag via low-rank updates and interpolation	9
Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap	9
Stability properties of a projector-splitting scheme for dynamical low rank approximation of random parabolic equations	9

Space-time CutFEM on overlapping meshes II: simple discontinuous mesh evolution	9
A semi-Lagrangian scheme for Hamilton–Jacobi–Bellman equations with oblique derivatives boundary conditions	8
Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains	8
Compression of boundary integral operators discretized by anisotropic wavelet bases	8
A matrix-theoretic spectral analysis of incompressible Navier–Stokes staggered DG approximations and a related spectrally based preconditioning approach	8
Monotone discretizations of levelset convex geometric PDEs	7
Finite element methods for the stretching and bending of thin structures with folding	7
On the adaptive Levin method	7
Error estimates for total-variation regularized minimization problems with singular dual solutions	7
Numerical dynamics of integrodifference equations	7
Weak convergence rates for temporal numerical approximations of the semilinear stochastic wave equation with multiplicative noise	7
Numerical approximation of variational problems with orthotropic growth	7
A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws	6
A unifying framework for tangential interpolation of structured bilinear control systems	6
Entropy inequalities for fully-discrete E-schemes: a sequel	6
The local discontinuous Galerkin method for a singularly perturbed convection–diffusion problem with characteristic and exponential layers	6
Maximal spaces for approximation rates in $$\ell ^1$$-regularization	6
Interior estimates for the virtual element method	6
On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation	6
Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations	6
A roadmap for Generalized Plane Waves and their interpolation properties	6
A posteriori error estimates for Radau IIA methods via maximal parabolic regularity	6
Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems	6
Stability and asymptotic analysis for instationary gas transport via relative energy estimates	6
Sparse harmonic transforms II: best s-term approximation guarantees for bounded orthonormal product bases in sublinear-time	6
On algebraically stabilized schemes for convection–diffusion–reaction problems	6
Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method	6
Riemannian acceleration with preconditioning for symmetric eigenvalue problems	6
Oscillation in a posteriori error estimation	6
High-order bounds-satisfying approximation of partial differential equations via finite element variational inequalities	6
Two-layer networks with the $$\text {ReLU}^k$$ activation function: Barron spaces and derivative approximation	6
Super-localization of spatial network models	6
Lattice enumeration via linear programming	6
An immersed Crouzeix–Raviart finite element method in 2D and 3D based on discrete level set functions	6
A structure-preserving parametric finite element method for geometric flows with anisotropic surface energy	5
Uniform boundary stabilization of a high-order finite element space discretization of the 1-d wave equation	5
Maximizing sum of coupled traces with applications	5
Orthogonality relations of Crouzeix–Raviart and Raviart–Thomas finite element spaces	5
Corrected trapezoidal rules for boundary integral equations in three dimensions	5
Goal-oriented adaptive finite element methods with optimal computational complexity	5
MDFEM: Multivariate decomposition finite element method for elliptic PDEs with uniform random diffusion coefficients using higher-order QMC and FEM	5
A Godunov type scheme and error estimates for scalar conservation laws with Panov-type discontinuous flux	5
Fast solution of incompressible flow problems with two-level pressure approximation	5
Fortin operator for the Taylor–Hood element	5
Moment-SoS methods for optimal transport problems	5
Numerical stability and tensor nuclear norm	5
Least-squares finite elements for distributed optimal control problems	5
Coercive second-kind boundary integral equations for the Laplace Dirichlet problem on Lipschitz domains	5
Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems	5
Error estimates for deep learning methods in fluid dynamics	4

A new parameter free partially penalized immersed finite element and the optimal convergence analysis	4
Correction to: Rigorous numerics for nonlinear heat equations in the complex plane of time	4
Fast evaluation of real and complex polynomials	4
On numerical approximations to fluid–structure interactions involving compressible fluids	4
Stabilization of loosely coupled schemes for 0D–3D fluid–structure interaction problems with application to cardiovascular modelling	4
A super-localized generalized finite element method	4
Numerical approximation of the stochastic Cahn–Hilliard equation near the sharp interface limit	4
Rigorous numerics for nonlinear heat equations in the complex plane of time	4
Numerical analysis of the SIMP model for the topology optimization problem of minimizing compliance in linear elasticity	4
A posteriori error analysis and adaptivity for high-dimensional elliptic and parabolic boundary value problems	4
New analysis of mixed FEMs for dynamical incompressible magnetohydrodynamics	4
Stochastic collocation method for computing eigenspaces of parameter-dependent operators	4
A stable local commuting projector and optimal hp approximation estimates in $$\varvec{H}(\textrm{curl})$$	4
Publisher Correction to: On the numerical stability of linear barycentric rational interpolation	4
Complete radiation boundary conditions for the Helmholtz equation II: domains with corners	4
Coercivity, essential norms, and the Galerkin method for second-kind integral equations on polyhedral and Lipschitz domains	4
Concentration in Lotka–Volterra parabolic equations: an asymptotic-preserving scheme	3
Wave scattering problems in exterior domains with the method of fundamental solutions	3
An iterative method for the solution of Laplace-like equations in high and very high space dimensions	3
Newton–Krylov-BDDC deluxe solvers for non-symmetric fully implicit time discretizations of the bidomain model	3
A generic construction for high order approximation schemes of semigroups using random grids	3
The effect of quadrature rules on finite element solutions of Maxwell variational problems	3
Energy relaxation approximation for compressible multicomponent flows in thermal nonequilibrium	3
Zhang neural networks: an introduction to predictive computations for discretized time-varying matrix problems	3
An error estimate for a finite-volume scheme for the Cahn–Hilliard equation with dynamic boundary conditions	3
Numerical approximation of control problems of non-monotone and non-coercive semilinear elliptic equations	3
A Hausdorff-measure boundary element method for acoustic scattering by fractal screens	3
A real triple dqds algorithm for the nonsymmetric tridiagonal eigenvalue problem	3
Entropy and convergence analysis for two finite volume schemes for a Nernst–Planck–Poisson system with ion volume constraints	3
A numerical investigation of Brockett’s ensemble optimal control problems	3
Efficient approximation of high-frequency Helmholtz solutions by Gaussian coherent states	3
Multilevel quasi-Monte Carlo for optimization under uncertainty	3
Grid-free weighted particle method applied to the Vlasov–Poisson equation	3
Nonnegative low rank tensor approximations with multidimensional image applications	3
Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations	3
Trefftz discontinuous Galerkin discretization for the Stokes problem	3
On the number of terms in the COS method for European option pricing	3
Optimal operator preconditioning for pseudodifferential boundary problems	3
Sensitivity of low-rank matrix recovery	3
Preconditioning techniques for the coupled Stokes–Darcy problem: spectral and field-of-values analysis	3
Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations	3
Stability of mixed FEMs for non-selfadjoint indefinite second-order linear elliptic PDEs	3
Stabilization-free HHO a posteriori error control	3
Statistical properties of BayesCG under the Krylov prior	3
Interpolation on the cubed sphere with spherical harmonics	2
Correction to: A sharp interface method using enriched finite elements for elliptic interface problems	2
Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine-Gordon equation	2
The pressure-wired Stokes element: a mesh-robust version of the Scott–Vogelius element	2
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver	2
New preconditioners for the Laplace and Helmholtz integral equations on open curves: analytical framework and numerical results	2
Finite element approximation of time-dependent mean field games with nondifferentiable Hamiltonians	2
Interpolation operators for parabolic problems	2
A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems	2
Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds	2
Krylov improvements of the Uzawa method for Stokes type operator matrices	2
Dynamical reduced basis methods for Hamiltonian systems	2
Fully computable a posteriori error bounds for eigenfunctions	2
Unconditionally positivity preserving and energy dissipative schemes for Poisson–Nernst–Planck equations	2
Stable generalized finite element method (SGFEM) for three-dimensional crack problems	2
Randomized block Krylov methods for approximating extreme eigenvalues	2
Correction to: Finite element error estimates in non-energy norms for the two-dimensional scalar Signorini problem	2
A framework for randomized time-splitting in linear-quadratic optimal control	2
Precision-aware deterministic and probabilistic error bounds for floating point summation	2
A discrete elasticity complex on three-dimensional Alfeld splits	2
A parallel-in-time approach for wave-type PDEs	2
A randomized operator splitting scheme inspired by stochastic optimization methods	2
Correction to: A note on Dekker’s FastTwoSum algorithm	2
A generalization of a theorem of Brass and Schmeisser	2
Spectral convergence of probability densities for forward problems in uncertainty quantification	2
A multipoint stress-flux mixed finite element method for the Stokes-Biot model	2
Asymptotic properties of Monte Carlo methods in elliptic PDE-constrained optimization under uncertainty	2
A convergence framework for optimal transport on the sphere	2
Circuits of ferromagnetic nanowires	2
Budget-limited distribution learning in multifidelity problems	2
Galerkin approximation of holomorphic eigenvalue problems: weak T-coercivity and T-compatibility	2