A nearly-conservative high-order Lagrange-Galerkin method for the resolution of scalar convection-dominated equations in non-divergence-free velocity fields

DOI10.1016/j.cma.2020.113366zbMath1506.65150OpenAlexW3081805467MaRDI QIDQ2020960

Rodolfo Bermejo, Manuel Colera, Jaime Carpio

Publication date: 26 April 2021

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2020.113366

zbMATH Keywords

finite element methodhigh-order methodsconvection-dominated problemsLagrange-Galerkinlocal projection stabilizationnon-divergence-free velocity field

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (5)

A mass-preserving two-step Lagrange-Galerkin scheme for convection-diffusion problems ⋮ A nearly-conservative, high-order, forward Lagrange-Galerkin method for the resolution of compressible flows on unstructured triangular meshes ⋮ A semi-Lagrangian meshfree Galerkin method for convection-dominated partial differential equations ⋮ A stable conservative Lagrange-Galerkin scheme to pure convection equations with mesh intersection ⋮ A nearly-conservative, high-order, forward Lagrange-Galerkin method for the resolution of scalar hyperbolic conservation laws

Uses Software

• Gmsh
• FACTORIZE
• Julia

Cites Work

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• A genuinely stable Lagrange-Galerkin scheme for convection-diffusion problems
• Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems
• On Koornwinder classical orthogonal polynomials in two variables
• An anisotropic, fully adaptive algorithm for the solution of convection-dominated equations with semi-Lagrangian schemes
• A second order in time local projection stabilized Lagrange-Galerkin method for Navier-Stokes equations at high Reynolds numbers
• An unconditionally stable fully conservative semi-Lagrangian method
• A nodal triangle-based spectral element method for the shallow water equations on the sphere
• Stabilized methods for compressible flows
• A mass-conservative characteristic finite element scheme for convection-diffusion problems
• A conservative nodal variational multiscale method for Lagrangian shock hydrodynamics
• Conservative interpolation between volume meshes by local Galerkin projection
• Enforcement of constraints and maximum principles in the variational multiscale method
• A\(_ 0\)-stability of variable stepsize BDF methods
• A local anisotropic adaptive algorithm for the solution of low-Mach transient combustion problems
• Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: theoretical framework and two-dimensional computations
• A comparison of interpolation grids over the triangle or the tetrahedron
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Spectral methods on triangles and other domains
• An introduction to finite element methods for transient advection problems
• A generalized particle search-locate algorithm for arbitrary grids
• A characteristic/finite element algorithm for time-dependent 3-D advection-dominated transport using unstructured grids.
• Strong and weak Lagrange-Galerkin spectral element methods for the shallow water equations
• Symmetric quadrature rules on a triangle
• An efficient characteristic Galerkin scheme for the advection equation in 3D.
• Evolution-Galerkin methods and their supraconvergence
• A Lagrangian finite element method for 3D compressible flow applications
• Local projection stabilized Lagrange-Galerkin methods for Navier-Stokes equations at high Reynolds numbers
• Pure Lagrangian and semi-Lagrangian finite element methods for the numerical solution of Navier-Stokes equations
• A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes
• A fully semi-Lagrangian discretization for the 2D incompressible Navier-Stokes equations in the vorticity-streamfunction formulation
• Modified Lagrange-Galerkin methods of first and second order in time for convection-diffusion problems
• Stabilized shock hydrodynamics. I: A Lagrangian method
• A vectorized particle tracer for unstructured grids
• Julia: A Fresh Approach to Numerical Computing
• Algorithm 930
• Runge-Kutta Methods with Minimum Error Bounds
• Gauss legendre quadrature formulas over a tetrahedron
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• A semi-Lagrangian-Galerkin projection scheme for convection equations
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• Stability of the Lagrange-Galerkin method with non-exact integration
• Convergence Analysis for a Class of High-Order Semi-Lagrangian Advection Schemes
• High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics
• A Second Order in Time Modified Lagrange--Galerkin Finite Element Method for the Incompressible Navier--Stokes Equations
• Anisotropic “Goal-Oriented” Mesh Adaptivity for Elliptic Problems
• An Explicit Sixth-Order Runge-Kutta Formula

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