Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-03T22:00:49.189565Z
Paper Citation Record · LEDGER
As of 19 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:2511.13217.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-03T22:00:49.189565Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
54 of 54 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 4287f329-fc00-4621-86a4-90d05b8d7bb2 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Coupled mode and finite element approximations of underwater sound propagation prob- lems in general stratified environments
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 693c5cea-4bfa-48ed-800d-a3d06087201b · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A two point boundary value problem with a rapidly oscillating solution
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8ae8f424-257b-42c0-8cb0-7715582511b8 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?
Reference 3
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5f4b219d-776d-4b5a-86bd-6be9e8d66834 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations On accuracy conditions for the numerical compu- tation of waves
Reference 4
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b79ff9b4-6f54-4e29-a319-5c4828e70801 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A space–time continuous and coercive formulation for the wave equation
Reference 5
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2471ba1b-27b6-4584-8e81-ecc5c2745d0a · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Wave-number-explicit bounds in time-harmonic scat- tering
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e56208c7-aba7-41ab-9139-d4186295a3f2 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations The virial theorem and the method of multipliers in spectral theory
Reference 7
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bea4ee2f-0cba-4028-8866-b3e01549ca1f · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations An efficient neural network method with plane wave activa- tion functions for solving Helmholtz equation
Reference 8
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 98b3239b-3b83-4edc-b361-b54131815303 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Sharp regularity coefficient estimates for complex-valued acous- tic and elastic Helmholtz equations
Reference 9
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8968cc2b-70cc-4c85-b168-81bbb3b846c7 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Evolution equations on non-flat waveguides
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1c04cfa0-58e8-4c66-9db5-d9d1f4c9dfb6 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Dautray and J.-L
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9c97befe-daec-47ee-ac5a-f477500da86a · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Frequency domain treatment of one-dimensional scalar waves
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 805918d4-cf13-4df6-b65e-dee7a1f9b2b1 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Unresolved cited work
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 99a870b8-5a11-4f28-b961-c56b670e60e3 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations hp-discontinuous Galerkin methods for the Helmholtz equation with large wave number
Reference 14
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 575e771a-adb3-4b95-96b0-0736de8ace0f · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Variational methods for underwater acoustic problems
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e1fbf4fa-bfbb-4e71-842e-1e4a415a6d41 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Unresolved cited work
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3455eeee-db77-45e0-9067-da7e58b3268b · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Givoli.Numerical methods for problems in infinite domains
Reference 17
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b6a18e0e-f688-467d-92c2-15085aa2e8c3 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A finite element method for solving Helmholtz type equations in waveguides and other unbounded domains
Reference 18
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 433e01d8-272c-41f5-b4c7-50fc4dff89b2 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Stability and finite element error analysis for the Helmholtz equa- tion with variable coefficients
Reference 19
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 04d07d74-5f28-4516-b6e7-b0657f60bf2a · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Grisvard.Elliptic problems in nonsmooth domains
Reference 20
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7a50dd62-fdf5-4b28-ac24-1abe2ca4300f · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations On controllability methods for the Helmholtz equation
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 48bca2ab-0d65-4923-b93a-aa6a9950ee55 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Wave decay for star-shaped obstacles inR 3: papers of Morawetz and Ralston revisited
Reference 22
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 37fc9bcd-9b1b-4941-92df-614746d2b2b3 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A survey of Trefftz methods for the Helmholtz equation
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7f53bd6a-3209-4706-9b05-f3f8b1bd5892 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Ihlenburg.Finite Element Analysis of Acoustic Scattering
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cbb4e0ce-7511-4511-89ef-2e4ec30ce2d5 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM
Reference 25
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bd266947-3c15-4ae6-ac2a-48fae9ad5a5b · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Exact non-reflecting boundary conditions
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9170222c-43d8-466c-a6e0-7d1fd16793e9 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Lanczos.The Variational Principles of Mechanics
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 646e9611-807d-40db-98dc-f45cb1b780d5 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Nonlinear wave equations in infinite waveguides
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation aa7688f3-7501-490f-8764-576389f4e9b2 · outbound
Reference 29
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a06fd295-09a3-4568-883a-2102783450a6 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations DeepXDE: a deep learning library for solving differential equations
Reference 30
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 85686a09-3d2c-46ae-9e42-0559cf6665e6 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Analysis and finite element methods for a fluid- solid interaction problem in one dimension
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b35892b2-ba4b-4c3b-b04e-2c2085a3010c · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
Reference 32
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4f1b75fa-f153-40b8-98cd-efb46128ae74 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations On Generalized Finite Element Methods
Reference 33
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 14e38eb7-a9e1-4471-9688-394f7fd568ef · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Nonlinear hyperbolic equations in infinite homo- geneous waveguides
Reference 34
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5e26a371-98cb-413f-a80a-486198efdc85 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Near- and far-field boundary conditions for a finite element method for the Helmholtz equation in axisymmetric problems of underwater acoustics
Reference 35
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4fbc994d-7330-436c-ad38-0636c3c0ad32 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Helmholtz equation with artificial boundary conditions in a two-dimensional waveguide
Reference 36
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5dc622ce-15d5-48da-9048-222539b8d924 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A finite element method with nonlocal boundary condi- tions for the Helmholtz equation with complex wavenumber in stratified waveguides
Reference 37
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d617851f-c760-421b-88eb-77708b43122b · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Is the Helmholtz Equation Really Sign-Indefinite?
Reference 38
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e26153e6-3219-41a2-9560-49c50f80f203 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Unresolved cited work
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cf949441-959b-4190-859c-f573c6cb3ccf · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations An inequality for the reduced wave operator and the jus- tification of geometrical optics
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 988f7381-642a-4af4-99f3-8cc39970f5b2 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations On the modes of decay for the wave equation in the exterior of a reflecting body
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 639f93e2-da19-421b-b888-f72168fc6e07 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Morrey–Campanato estimates for Helmholtz equations
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7e0801c7-62aa-4719-8905-552e1f44a1f5 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Eliminating the pollution effect in Helmholtz problems by local subscale cor- rection
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a907a782-660c-4aad-b574-dcb980b35214 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Reference 44
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b96a874b-8a2c-444f-ae84-7396b31c1bf5 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A refined finite element convergence theory for highly indefinite Helmholtz problems
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation adba2b0f-8882-4b99-9c53-4076ee3056f2 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Stability estimate for the Helmholtz equation with rapidly jumping coefficients
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 06077c99-d0ce-45c4-96ef-4e13d3474921 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
Reference 47
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5795e665-174b-4ea3-aba1-bcb10f95bced · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Feasibility study on solving the Helmholtz equation in 3D with PINNs
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d5ecc725-2850-4bc4-862f-265504bb2b2f · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A perfectly matched layer for the Helmholtz equation in a semi- infinite strip
Reference 49
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b10b579b-c1c5-4087-a3c6-f3f49f547f6a · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A versatile framework to solve the Helmholtz equation using physics-informed neural networks
Reference 50
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a62018f4-45bb-41fb-a54f-d7f826026949 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations A new frequency- uniform coercive boundary integral equation for acoustic scattering
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 4f5693ca-176a-4ea7-932a-921ba419bff8 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Morawetz inequalities
Reference 52
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0b78ff36-ac9a-4711-8738-869dc2eac0c6 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Tao.Nonlinear dispersive equations
Reference 53
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b23f8350-aa6b-4e54-b323-39e829f8b164 · outbound
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations Unresolved cited work
Reference 54
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
No inbound Pith citation observations are available.