Adaptive multiresolution discontinuous Galerkin schemes for conservation laws

DOI10.1090/S0025-5718-2013-02732-9zbMath1282.65118MaRDI QIDQ2862523

Siegfried Müller, Nune Hovhannisyan, Roland Schäfer

Publication date: 15 November 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

numerical resultsnonlinear hyperbolic conservation lawsdiscontinuous Galerkin schemesperturbation errormultiresolution based

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Numerical methods for wavelets (65T60) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items

A wavelet-free approach for multiresolution-based grid adaptation for conservation laws ⋮ An efficient algorithm based on the multi-wavelet Galerkin method for telegraph equation ⋮ Multiwavelet-based grid adaptation with discontinuous Galerkin schemes for shallow water equations ⋮ Sparse grid discontinuous Galerkin methods for high-dimensional elliptic equations ⋮ Multiwavelet discontinuous Galerkin \(h\)-adaptive shallow water model ⋮ Capitalizing on superconvergence for more accurate multi-resolution discontinuous Galerkin methods ⋮ On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets ⋮ Automated Parameters for Troubled-Cell Indicators Using Outlier Detection ⋮ Enhanced MultiResolution Analysis for MultiDimensional Data Utilizing Line Filtering Techniques ⋮ On the sparse multiscale representation of <scp>2‐D</scp> Burgers equations by an efficient algorithm based on multiwavelets ⋮ A new family of means: the generalized weighted power means and applications ⋮ \(h\)-adaptation for high-order discontinuous Galerkin schemes built on local multiwavelet analysis ⋮ An Adaptive Multiresolution Discontinuous Galerkin Method for Time-Dependent Transport Equations in Multidimensions ⋮ Global sensitivity analysis using multi-resolution polynomial chaos expansion for coupled Stokes-Darcy flow problems ⋮ Analysis and simulation of a new multi-component two-phase flow model with phase transitions and chemical reactions ⋮ An adaptive multiresolution interior penalty discontinuous Galerkin method for wave equations in second order form ⋮ An Adaptive Multiresolution Discontinuous Galerkin Method with Artificial Viscosity for Scalar Hyperbolic Conservation Laws in Multidimensions ⋮ Hyperbolic stochastic Galerkin formulation for the \(p\)-system ⋮ On the multiwavelets Galerkin solution of the Volterra-Fredholm integral equations by an efficient algorithm ⋮ A novel and efficient numerical algorithm for solving 2D Fredholm integral equations ⋮ A class of non-oscillatory direct-space-time schemes for hyperbolic conservation laws ⋮ Adaptive multiresolution semi-Lagrangian discontinuous Galerkin methods for the Vlasov equations ⋮ Adaptive multiresolution discontinuous Galerkin schemes for conservation laws: multi-dimensional case ⋮ Abel's integral operator: sparse representation based on multiwavelets ⋮ Coupling of compressible Euler equations ⋮ Multiwavelets and Jumps in DG Approximations ⋮ A high-order discontinuous Galerkin discretization with multiwavelet-based grid adaptation for compressible flows ⋮ On a multiwavelet spectral element method for integral equation of a generalized Cauchy problem

Uses Software

• igpm_t_lib

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An adaptive multiscale finite volume solver for unsteady and steady state flow computations
• Adjoint-based \(h\)-\(p\) adaptive discontinuous Galerkin methods for the 2D compressible Euler equations
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
• \(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Adaptive multiscale schemes for conservation laws
• Adaptive solution of partial differential equations in multiwavelet bases
• Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations.
• A high-order discontinuous Galerkin discretization with multiwavelet-based grid adaptation for compressible flows
• Strong Stability-Preserving High-Order Time Discretization Methods
• Multiresolution Analysis and Supercompact Multiwavelets
• Discrete Multiresolution Analysis Using Hermite Interpolation: Biorthogonal Multiwavelets
• On the stability of fully adaptive multiscale schemes for conservation laws using approximate flux and source reconstruction strategies
• Refinement and Connectivity Algorithms for Adaptive Discontinuous Galerkin Methods
• The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• Quasimonotone Schemes for Scalar Conservation Laws Part I
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• A theory for multiresolution signal decomposition: the wavelet representation
• New Trends in Multiresolution and Adaptive Methods for Convection-Dominated Problems
• Convergence of Generalized MUSCL Schemes
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• A Class of Bases in $L^2$ for the Sparse Representation of Integral Operators
• Biorthogonal bases of compactly supported wavelets
• Error Bounds for Fractional Step Methods for Conservation Laws with Source Terms
• An Adaptive Discontinuous Galerkin Technique with an Orthogonal Basis Applied to Compressible Flow Problems
• Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
• Finite Volume Methods for Hyperbolic Problems
• Fully adaptive multiresolution finite volume schemes for conservation laws
• hp‐Discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity
• Multiresolution Representation of Data: A General Framework
• Discontinuous solutions of non-linear differential equations
• Error Control for a Class of Runge–Kutta Discontinuous Galerkin Methods for Nonlinear Conservation Laws
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
• Multiresolution schemes for conservation laws