The lack of error estimators for dynamic iteration methods coupled with finite element schemes

The gap

Evidence profile

Sourced from the stated research gap and future-work section of the source papers, classified as general, spanning 4 journals.

Supporting evidence — 5 representative gaps

• Splitting schemes for ODEs with goal–oriented error estimation (2026) · BIT Numerical Mathematics · doi

  The lack of error estimators for dynamic iteration methods coupled with finite element schemes. The need for adaptive and flexible discretization of the time domain.

  generalstated research gapevidence 5/5
  Keywords: lack error estimators dynamic iteration methods coupled finite
• On discrete Sobolev inequalities for nonconforming finite elements under a semiregular mesh condition (2026) · IMA Journal of Numerical Analysis · doi

  The authors suggest that the new geometric parameter can be useful in adaptive finite element methods. Further research can be conducted to apply the discrete Sobolev inequality to a wide range of problems.

  generalfuture-work sectionevidence 5/5
  Keywords: authors suggest new geometric parameter useful adaptive finite
• Asymptotic Lower Bounds of Eigenvalues for the Steklov Eigenvalue Problem (2026) · Communications on Applied Mathematics and Computation · doi

  The lack of methods that can provide lower bound approximations of eigenvalues. The limitations of existing conforming finite element methods and finite element methods tailored to approximating the Steklov eigenvalue problems.

  generalstated research gapevidence 5/5
  Keywords: lack methods provide lower bound approximations eigenvalues limitations
• Asymptotic Lower Bounds of Eigenvalues for the Steklov Eigenvalue Problem (2026) · Communications on Applied Mathematics and Computation · doi

  To further develop the nonconforming finite element method to solve the Steklov eigenvalue problems. To apply the method to more complex domains and problems. To improve the numerical scheme to compute lower bounds of eigenvalues.

  generalfuture-work sectionevidence 5/5
  Keywords: further develop nonconforming finite element method solve steklov
• Pointwise a Posteriori Error Estimators for Multiple and Clustered Eigenvalue Computations (2026) · Journal of Scientific Computing · doi

  The lack of efficient and reliable error estimators for multiple and clustered eigenvalue computations. The limitation of standard finite element methods on quasi-uniform meshes when solving elliptic partial differential equations with local singularities in the exact solution. The need for quasi-optimal adaptive finite element methods for elliptic eigenvalue problems.

  generalstated research gapevidence 5/5
  Keywords: lack efficient reliable error estimators multiple clustered eigenvalue

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