An adaptive finite element method for semilinear parabolic interface problems with nonzero flux jump

DOI10.1016/j.apnum.2020.03.001zbMath1436.65188OpenAlexW3009686355MaRDI QIDQ1986168

Tanushree Ray, Rajen Kumar Sinha

Publication date: 7 April 2020

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2020.03.001

zbMATH Keywords

adaptive algorithma posteriori error estimatesparabolic interface problemsemilinear

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Semilinear parabolic equations (35K58)

Uses Software

• ALBERT
• FreeFem++

Cites Work

• A posteriori error analysis of two-step backward differentiation formula finite element approximation for parabolic interface problems
• A conservative and monotone mixed-hybridized finite element approximation of transport problems in heterogeneous domains
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• Adaptive finite elements for a linear parabolic problem
• A review of a posteriori error estimation techniques for elasticity problems
• Discontinuous Galerkin Methods for Mass Transfer through Semipermeable Membranes
• Robust residual- and recovery-based a posteriori error estimators for interface problems with flux jumps
• Robusta posteriorierror estimates for finite element discretizations of the heat equation with discontinuous coefficients
• Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements
• A‐posteriori error estimates for the finite element method
• Data Oscillation and Convergence of Adaptive FEM
• On the Efficiency of Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
• An adaptive finite element algorithm with reliable and efficient error control for linear parabolic problems
• A Convergent Adaptive Algorithm for Poisson’s Equation
• New development in freefem++
• The Mathematical Theory of Finite Element Methods
• Galerkin Finite Element Methods for Parabolic Problems
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