Finite element approximation for time-dependent diffusion with measure-valued source

DOI10.1007/s00211-012-0474-8zbMath1266.65172OpenAlexW2142732983MaRDI QIDQ695292

Matthias K. Gobbert, David W. Trott, Thomas I. Seidman, Martin Kružík

Publication date: 20 December 2012

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11603/11665

zbMATH Keywords

numerical resultsfinite elementerror estimateconvergence ratediffusion problemcalcium flow in heart cellsmeasure-valued source term

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order parabolic equations (35K35) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Physiological flow (92C35)

Related Items (7)

Adaptive finite element methods for an optimal control problem involving Dirac measures ⋮ Linkages of calcium-induced calcium release in a cardiomyocyte simulated by a system of seven coupled partial differential equations ⋮ Piecewise polynomial interpolation in Muckenhoupt weighted Sobolev spaces and applications ⋮ A memory‐efficient finite volume method for advection‐diffusion‐reaction systems with nonsmooth sources ⋮ Modelling with measures: approximation of a mass-emitting object by a point source ⋮ Optimal error estimate of elliptic problems with Dirac sources for discontinuous and enriched Galerkin methods ⋮ Insight into spontaneous recurrent calcium waves in a 3-D cardiac cell based on analysis of a 1-D deterministic model

Uses Software

• COMSOL

Cites Work

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• A memory-efficient finite element method for systems of reaction--diffusion equations with non-smooth forcing
• Caractérisation de quelques espaces d'interpolation
• Finite element convergence for singular data
• Long-Time Simulations on High Resolution Meshes to Model Calcium Waves in a Heart Cell
• Error Estimates for Semidiscrete Finite Element Approximations of Linear and Semilinear Parabolic Equations Under Minimal Regularity Assumptions
• Galerkin Finite Element Methods for Parabolic Problems
• Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order

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