Methods Based on Polynomial Chaos for Quadratic Delay Differential Equations With Random Parameters
PAMM, Volume 26, Issue 1, March 2026.ABSTRACT We consider systems of delay differential equations (DDEs), including a single delay and a quadratic right‐hand side. In a system, parameters are replaced by random variables to perform an uncertainty quantification. Thus the solution of the DDEs becomes a random process, which can be represented by a series of the generalised polynomial chaos.
Roland Pulch
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A posteriori error approximation in discontinuous Galerkin method on polygonal meshes in elliptic problems. [PDF]
Sci Rep, 2023 Jaśkowiec J, Pamin J.
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AIChE Journal, Volume 72, Issue 2, February 2026.Abstract Here, we introduce a calibration‐less bonded‐sphere model to describe three‐dimensional, linear elastic, highly deformable particles. Voronoi tessellation is used to partition a particle into multiple sub‐spheres, generating a virtual bond network that mimics the mechanical properties of the original particle.
Runhui Zhang +2 more
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Abstract and Applied Analysis, 2014 We propose, analyze, and test a fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional diffusion equation. The proposed method is based on a finite difference scheme in time and local discontinuous Galerkin methods ...
Leilei Wei, Xindong Zhang
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Finite Element Method for the Solution of a Time-Dependent Heat-Like Lane-Emden Equation
Universal Journal of Mathematics and Applications, 2018 In this study, finite element method (FEM) with Galerkin Formula is applied to find the numerical solution of a time-dependent heat-like Lane-Emden equation. An example is solved to assess the accuracy of the method.
Mehmet Fatih Uçar
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Analysis of the Element-Free Galerkin Method with Penalty for Stokes Problems. [PDF]
Entropy (Basel), 2022 Zhang T, Li X.
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Convergence properties of dynamic mode decomposition for analytic interval maps
Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 179-206, February 2026.Abstract Extended dynamic mode decomposition (EDMD) is a data‐driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method with N$N$ functions and a quadrature method with M$M$ quadrature nodes.
Elliz Akindji +3 more
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The numerical solution of a mathematical model of the Covid-19 pandemic utilizing a meshless local discrete Galerkin method. [PDF]
Eng Comput, 2022 Asadi-Mehregan F, Assari P, Dehghan M.
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Locally Adaptive Non‐Hydrostatic Shallow Water Extension for Moving Bottom‐Generated Waves
International Journal for Numerical Methods in Fluids, Volume 98, Issue 2, Page 159-173, February 2026.This study proposes a locally adaptive non‐hydrostatic model, which is based on the non‐hydrostatic extension of the shallow water equations (SWE) with a quadratic pressure relation, and applies it to wave propagation generated by a moving bottom. To obtain the locally adaptive model, we investigate several potential adaptivity criteria based on the ...
Kemal Firdaus, Jörn Behrens
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Comparison of SUPG with Bubble Stabilization Parameters and the Standard SUPG
Abstract and Applied Analysis, 2014 We study a streamline upwind Petrov-Galerkin method (SUPG) with bubble stabilization coefficients on quasiuniform triangular meshes. The new algorithm is a consistent Petrov-Galerkin method and shows similar numerical performances as the standard SUPG ...
Xiaowei Liu, Jin Zhang
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