Optimal error bounds for partially penalized immersed finite element methods for parabolic interface problems

DOI10.1016/j.cam.2019.112401zbMath1428.65045OpenAlexW2969645020WikidataQ127354784 ScholiaQ127354784MaRDI QIDQ2332708

Qiao Zhuang, Tao Lin

Publication date: 5 November 2019

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2019.112401

zbMATH Keywords

parabolic interface problemsoptimal convergencelow regularityimmersed finite element methods

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (13)

Optimal convergence analysis of the energy-preserving immersed weak Galerkin method for second-order hyperbolic interface problems in inhomogeneous media ⋮ Optimal error bound for immersed weak Galerkin finite element method for elliptic interface problems ⋮ Semi and fully discrete error analysis for elastodynamic interface problems using immersed finite element methods ⋮ A two-grid immersed finite element method with the Crank-Nicolson time scheme for semilinear parabolic interface problems ⋮ A unified immersed finite element error analysis for one-dimensional interface problems ⋮ Fully discrete least-squares spectral element method for parabolic interface problems ⋮ A class of nonconforming immersed finite element methods for Stokes interface problems ⋮ Unnamed Item ⋮ A family of two-grid partially penalized immersed finite element methods for semi-linear parabolic interface problems ⋮ A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces ⋮ Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis ⋮ Optimal convergence analysis of a linearized second-order BDF-PPIFE method for semi-linear parabolic interface problems ⋮ Immersed finite element method for time fractional diffusion problems with discontinuous coefficients

Cites Work

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• A numerical method for solving variable coefficient elliptic equation with interfaces
• Composite finite elements for elliptic boundary value problems with discontinuous coefficients
• New Cartesian grid methods for interface problems using the finite element formulation
• Immersed finite element method of lines for moving interface problems with nonhomogeneous flux jump
• Partially penalized immersed finite element methods for parabolic interface problems
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• Approximation capability of a bilinear immersed finite element space
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
• Poincaré--Friedrichs Inequalities for Piecewise H¹ Functions
• An immersed finite element space and its approximation capability
• Immersed finite element methods for parabolic equations with moving interface
• Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
• Finite Element Methods and Their Applications
• Finite elements. Theory, fast solvers and applications in elasticity theory

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