Convergence rates of the DPG method with reduced test space degree

DOI10.1016/j.camwa.2014.08.004zbMath1364.65239arXiv1408.6599OpenAlexW2038386729MaRDI QIDQ2628400

T. A. Bouma, Jay Gopalakrishnan, Ammar Harb

Publication date: 2 June 2017

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

Full work available at URL: https://arxiv.org/abs/1408.6599

zbMATH Keywords

least-squaresduality argumentdiscontinuous Petrov-GalerkinDPG methodAubin-Nitschestrang lemma

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (19)

Local analysis of HDG methods for convection-dominated diffusion problems ⋮ Analysis of backward Euler primal DPG methods ⋮ Low-order dPG-FEM for an elliptic PDE ⋮ A first order system least squares method for the Helmholtz equation ⋮ Nonlinear discontinuous Petrov-Galerkin methods ⋮ Reduced test spaces for DPG methods using rectangular elements ⋮ Efficient discretization and preconditioning of the singularly perturbed reaction-diffusion problem ⋮ Discontinuous Petrov-Galerkin approximation of eigenvalue problems ⋮ The DPG-star method ⋮ Approximation properties of primal discontinuous Petrov-Galerkin method on general quadrilateral meshes ⋮ Superconvergence of DPG approximations in linear elasticity ⋮ Superconvergence in a DPG method for an ultra-weak formulation ⋮ A Scalable Preconditioner for a Primal Discontinuous Petrov--Galerkin Method ⋮ Optimal Convergence Rates for Adaptive Lowest-Order Discontinuous Petrov--Galerkin Schemes ⋮ Breaking spaces and forms for the DPG method and applications including Maxwell equations ⋮ Asymptotically exact a posteriori error estimators for first-order div least-squares methods in local and global \(L_2\) norm ⋮ Notes on a saddle point reformulation of mixed variational problems ⋮ Analysis of FEAST spectral approximations using the DPG discretization ⋮ Superconvergent DPG methods for second-order elliptic problems

Uses Software

• DOLFIN
• FEniCS

Cites Work

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• Automated solution of differential equations by the finite element method. The FEniCS book
• Ein Kriterium für die Quasi-Optimalität des Titzschen Verfahrens
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• DOLFIN
• Analysis of the DPG Method for the Poisson Equation
• A non-conforming piecewise quadratic finite element on triangles
• Mixed and Hybrid Finite Element Methods
• Primal Hybrid Finite Element Methods for 2nd Order Elliptic Equations
• Adaptive Petrov--Galerkin Methods for First Order Transport Equations
• A Petrov-Galerkin discretization with optimal test space of a mild-weak formulation of convection-diffusion equations in mixed form
• A Posteriori Error Control for DPG Methods
• Dispersive and Dissipative Errors in the DPG Method with Scaled Norms for Helmholtz Equation

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