A parameter-free smoothness indicator for high-resolution finite element schemes

DOI10.2478/s11533-013-0254-4zbMath1273.65145OpenAlexW2029300779MaRDI QIDQ360327

Friedhelm Schieweck, Dmitri Kuzmin

Publication date: 26 August 2013

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-013-0254-4

zbMATH Keywords

algorithmfinite elementsmaximum principlesnumerical examplesgradient recoverysmoothness indicatorsslope limitingflux-corrected transport\(p\)-adaptationconvection equation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) First-order hyperbolic equations (35L02)

Related Items

A comparison of artificial viscosity, limiters, and filters, for high order discontinuous Galerkin solutions in nonlinear settings, A new vertex-based limiting approach for nodal discontinuous Galerkin methods on arbitrary unstructured meshes, Matrix-free subcell residual distribution for Bernstein finite elements: monolithic limiting, High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation, Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements, The Reference Solution Approach to Hp-Adaptivity in Finite Element Flux-Corrected Transport Algorithms, A partition of unity approach to adaptivity and limiting in continuous finite element methods, Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting, Hierarchical slope limiting in explicit and implicit discontinuous Galerkin methods, p-adaptive discontinuous Galerkin method for the shallow water equations with a parameter-free error indicator

Cites Work

• Unnamed Item
• Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion
• Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations
• Fully multidimensional flux-corrected transport algorithms for fluids
• A vertex-based hierarchical slope limiter for \(p\)-adaptive discontinuous Galerkin methods
• Explicit and implicit FEM-FCT algorithms with flux linearization
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws.
• Flux correction tools for finite elements
• A local projection stabilization method with shock capturing and diagonal mass matrix for solving non-stationary transport dominated problems
• A simple error estimator and adaptive procedure for practical engineerng analysis
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• The superconvergent patch recovery anda posteriori error estimates. Part 2: Error estimates and adaptivity
• On the discontinuous Galerkin method for the numerical solution of compressible high-speed flow
• High-Resolution Conservative Algorithms for Advection in Incompressible Flow
• Slope limiting for discontinuous Galerkin approximations with a possibly non‐orthogonal Taylor basis
• A Comparison of Troubled-Cell Indicators for Runge--Kutta Discontinuous Galerkin Methods Using Weighted Essentially Nonoscillatory Limiters