Breaking spaces and forms for the DPG method and applications including Maxwell equations

From MaRDI portal
Publication:520844

DOI10.1016/j.camwa.2016.05.004zbMath1359.65249arXiv1507.05428OpenAlexW1955273710MaRDI QIDQ520844

Yong-Cai Geng, Sumit K. Garg

Publication date: 6 April 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.05428




Related Items (98)

Equivalence between the DPG method and the exponential integrators for linear parabolic problemsA hybrid mimetic spectral element method for three-dimensional linear elasticity problemsAnalysis of backward Euler primal DPG methodsA space-time DPG method for the heat equationHybridization and postprocessing in finite element exterior calculusA stable space-time FE method for the shallow water equationsA stable FE method for the space-time solution of the Cahn-Hilliard equationAdaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order MethodsA first order system least squares method for the Helmholtz equationThe Skeleton Reduction for Finite Element Substructuring MethodsNonlinear discontinuous Petrov-Galerkin methodsDPG methods for a fourth-order div problemAn \(L^p\)-DPG method with application to 2D convection-diffusion problemsA low-order discontinuous Petrov-Galerkin method for the Stokes equationsAn adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagneticsA DPG method for shallow shellsModel and computational advancements to full vectorial Maxwell model for studying fiber amplifiersEditorial: Minimum residual and least squares finite element methods IIReduced test spaces for DPG methods using rectangular elementsConstruction of DPG Fortin operators for second order problemsAn adaptive DPG method for high frequency time-harmonic wave propagation problemsDeveloping and analyzing a finite element method for simulating wave propagation in graphene-based absorberEfficient discretization and preconditioning of the singularly perturbed reaction-diffusion problemError representation of the time-marching DPG schemeOn perfectly matched layers for discontinuous Petrov-Galerkin methodsCombining the DPG method with finite elementsA Discontinuous Petrov–Galerkin Method for Reissner–Mindlin PlatesScalable DPG multigrid solver for Helmholtz problems: a study on convergenceA DPG method for the quad-curl problemCombining DPG in space with DPG time-marching scheme for the transient advection-reaction equationDiscontinuous Petrov-Galerkin approximation of eigenvalue problemsThe DPG-star methodOn a relation of discontinuous Petrov-Galerkin and least-squares finite element methodsHilbert complexes: analysis, applications, and discretizations. Abstracts from the workshop held June 19--25, 2022Robust DPG Test Spaces and Fortin Operators—The \(\boldsymbol{H^1}\) and \({\boldsymbol{H}}\boldsymbol{(\mathrm{div})}\) CasesCoupled variational formulations of linear elasticity and the DPG methodologySuperconvergence of DPG approximations in linear elasticityThe DPG method for the convection-reaction problem, revisitedA new time-domain finite element method for simulating surface plasmon polaritons on graphene sheetsRobust DPG Methods for Transient Convection-DiffusionAn implicit-in-time DPG formulation of the 1D1V Vlasov-Poisson equationsA 3D DPG Maxwell approach to nonlinear Raman gain in fiber laser amplifiersA variational multiscale method derived from an adaptive stabilized conforming finite element method via residual minimization on dual normsSolving minimal residual methods in \(W^{-1,p'}\) with large exponents \(p\)A DPG method for planar div-curl problemsNew periodic wave, cross-kink wave and the interaction phenomenon for the Jimbo-Miwa-like equationOn the stability of DPG formulations of transport equationsA DPG Framework for Strongly Monotone OperatorsConstruction of DPG Fortin operators revisitedGoal-oriented error estimation for the automatic variationally stable FE method for convection-dominated diffusion problemsAn ultraweak formulation of the Kirchhoff–Love plate bending model and DPG approximationSuperconvergence in a DPG method for an ultra-weak formulationA Scalable Preconditioner for a Primal Discontinuous Petrov--Galerkin MethodOptimal Convergence Rates for Adaptive Lowest-Order Discontinuous Petrov--Galerkin SchemesA discontinuous Petrov-Galerkin method for compressible Navier-Stokes equations in three dimensionsIsogeometric analysis for explicit elastodynamics using a dual-basis diagonal mass formulationAnalysis and application of an equivalent Berenger's PML modelA time-stepping DPG scheme for the heat equationA DPG-based time-marching scheme for linear hyperbolic problemsAn unconditionally stable space-time FE method for the Korteweg-de Vries equationAdaptive \(w\)-refinement: a new paradigm in isogeometric analysisNumerical analysis of a finite element method for the electromagnetic concentrator modelA robust DPG method for large domainsA quasi-optimal test norm for a DPG discretization of the convection-diffusion equationNotes on a saddle point reformulation of mixed variational problemsThe discontinuous Petrov-Galerkin methodology for the mixed multiscale finite element methodThe double adaptivity paradigm. (How to circumvent the discrete inf-sup conditions of Babuška and Brezzi)Ultraweak formulation of linear PDEs in nondivergence form and DPG approximationA numerical study of the pollution error and DPG adaptivity for long waveguide simulationsConstruction and application of algebraic dual polynomial representations for finite element methods on quadrilateral and hexahedral meshesA least-squares formulation of the moving discontinuous Galerkin finite element method with interface condition enforcementAn \(L^p\)-DPG method for the convection-diffusion problemAnalysis of non-conforming DPG methods on polyhedral meshes using fractional Sobolev normsTime-stepping DPG formulations for the heat equationGenerating probability distributions on intervals and spheres with application to finite element methodTwo new finite element schemes and their analysis for modeling of wave propagation in grapheneA locking-free DPG scheme for Timoshenko beamsA Spacetime DPG Method for the Schrödinger EquationThe DPG methodology applied to different variational formulations of linear elasticityUsing a DPG method to validate DMA experimental calibration of viscoelastic materialsDiscrete least-squares finite element methodsHigh-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulationsA priori and computable a posteriori error estimates for an HDG method for the coercive Maxwell equationsGoal-Oriented Adaptive Mesh Refinement for Discontinuous Petrov--Galerkin MethodsAdaptive Mixed Finite Element Methods for Non-self-adjoint Indefinite Second-Order Elliptic PDEs with Optimal RatesAnalysis of FEAST spectral approximations using the DPG discretizationRecent advances in least-squares and discontinuous Petrov-Galerkin finite element methodsAdaptive strategies for transport equationsSpace-time discontinuous Petrov-Galerkin methods for linear wave equations in heterogeneous mediaSuperconvergent DPG methods for second-order elliptic problemsFast integration of DPG matrices based on sum factorization for all the energy spacesCamellia: a rapid development framework for finite element solversAlternative enriched test spaces in the DPG method for singular perturbation problemsThe discrete Steklov-Poincaré operator using algebraic dual polynomialsAn ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximationLow-Order Discontinuous Petrov--Galerkin Finite Element Methods for Linear ElasticityNonlinear Reduced Models for State and Parameter EstimationMINRES for Second-Order PDEs with Singular Data



Cites Work


This page was built for publication: Breaking spaces and forms for the DPG method and applications including Maxwell equations