Hybridized discontinuous Galerkin method for elliptic interface problems: error estimates under low regularity assumptions of solutions

DOI10.1007/s10915-018-0678-xzbMath1401.65134arXiv1701.00897OpenAlexW2790020201MaRDI QIDQ1785508

Norikazu Saito, Masaru Miyashita

Publication date: 28 September 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.00897

zbMATH Keywords

discontinuous Galerkin methoderror estimateelliptic interface problemsfractional order Sobolev space

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

Pressure robust hybrid mixed finite element method for Darcy–Forchheimer model, Superconvergence of the lowest-order weak Galerkin finite element method for elliptic interface problems, A Stable and Convergent Hybridized Discontinuous Galerkin Method for Time-Fractional Telegraph Equations, Hybridized CutFEM for Elliptic Interface Problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Weak Galerkin methods for second order elliptic interface problems
• A finite element method for interface problems in domains with smooth boundaries and interfaces
• Finite element methods and their convergence for elliptic and parabolic interface problems
• Adaptive finite element methods for elliptic equations with non-smooth coefficients
• Discontinuous Galerkin FEM of hybrid type
• Hybridized discontinuous Galerkin method with lifting operator
• A high-order hybridizable discontinuous Galerkin method for elliptic interface problems
• Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations
• Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
• On the finite element approximation of functions with noninteger derivatives
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• An Unfitted Discontinuous Galerkin Method Applied to Elliptic Interface Problems
• The Mathematical Theory of Finite Element Methods
• Regularity results for Laplace interface problems in two dimensions
• A posteriori error estimators for elliptic equations with discontinuous coefficients