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Frequency convergence characteristics of lumped mass Galerkin meshfree methods
Due to the considerable complexity of meshfree approximants, there still lacks a rational theoretical estimate on the frequency accuracy of lumped...
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Meshfree Galerkin Methods
The Finite Element Method based on a Lagrangian description of the differential equation is mostly used to simulate the behavior of solids under...
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High-order Accurate Beam Models Based on Discontinuous Galerkin Methods
A novel high-order accurate approach to the analysis of beam structures with bulk and thin-walled cross-sections is presented. The approach is based...
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Enforcing conserved quantities in Galerkin truncation and finite volume discretization
Finite-dimensional truncations are routinely used to approximate partial differential equations (PDEs), either to obtain numerical solutions or to...
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Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations
In this paper, we present a mesh adaptation algorithm for the unsteady compressible Navier-Stokes equations under the framework of local...
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Coupled response of sandwich beams on the nonlinear foundation under Galerkin truncation convergence criterion
Coupled vibration response of the beam on nonlinear foundations is of great theoretical significance in the field of engineering. Due to its complex...
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Dynamics of a Fluid-Conveying Pipe by a Hybrid Method Combining Differential Transformation and Galerkin Discretization
A new hybrid method combining differential transformation and Galerkin discretization is proposed to investigate the dynamics of a fluid-conveying...
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Efficiency analysis of discontinuous Galerkin approaches for the application onto quantum Liouville-type equations
The simulation of nanodevices is computationally inefficient with current algorithms. The discontinuous Galerkin approach has been demonstrated in...
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Galerkin spectral estimation of vortex-dominated wake flows
AbstractWe propose a technique for performing spectral (in time) analysis of spatially-resolved flowfield data, without needing any temporal...
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The Analysis of Higher Order Nonlinear Vibrations of an Elastic Beam with the Extended Galerkin Method
MotivationThe analysis of vibrations of an elastic beam is one of the persistently challenging problems in engineering and mathematics. The...
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A Comparison of Matrix-Free Isogeometric Galerkin and Collocation Methods for Karhunen–Loève Expansion
Numerical computation of the Karhunen–Loève expansion is computationally challenging in terms of both memory requirements and computing time. We...
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A robust implicit high-order discontinuous Galerkin method for solving compressible Navier-Stokes equations on arbitrary grids
The primary impediments impeding the implementation of high-order methods in simulating viscous flow over complex configurations are robustness and...
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One Line of Development of the Galerkin Projection Method in Problems of Stationary Solid Mechanics (Review)
One of the line of development of the projective Galerkin method intended for efficient solution of problems with a large number of independent...
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POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier–Stokes equations
We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems...
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Accuracy assessment of discontinuous Galerkin spectral element method in simulating supersonic free jets
The study performs large eddy simulations of supersonic free jet flows using the discontinuous Galerkin spectral element method (DGSEM). The main...
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A truly meshless approach to structural topology optimization based on the Direct Meshless Local Petrov–Galerkin (DMLPG) method
With a wide applicability in several types of engineering problems, topology optimization is one of the most interesting fields of structural...
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Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods
The success of mixed finite element methods (FEM) in the linear elasticity with focus on the accuracy of the stress variable on the one hand and...
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A simple a posteriori indicator for discontinuous Galerkin method on unstructured grids
A simple and efficient troubled-cell indicator based on a posteriori limiting paradigm is proposed for the discontinuous Galerkin (DG) method on the...
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Comparative Study Between Visibility and Diffraction Methods for LEFM in Element Free Galerkin Method
Element-free Galerkin (EFG) offers a numerical recourse to solve physical problems formulated in terms of partial differential equations. In...
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Numerical Dissipation Rate Analysis of Finite-Volume and Continuous-Galerkin Methods for LES of Combustor Flow-Field
A growing body of literature indicates that element-based high-order methods can exhibit considerable accuracy/cost benefit over conventional...
