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Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces
Author(s) -
Kovács Balázs,
Power Guerra Christian Andreas
Publication year - 2016
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22047
Subject(s) - mathematics , discretization , convergence (economics) , partial differential equation , runge–kutta methods , integrator , stability (learning theory) , partial derivative , finite element method , mathematical analysis , ordinary differential equation , space (punctuation) , surface (topology) , differential equation , geometry , computer science , computer network , physics , bandwidth (computing) , machine learning , economic growth , economics , thermodynamics , operating system
Convergence results are shown for full discretizations of quasilinear parabolic partial differential equations on evolving surfaces. As a semidiscretization in space the evolving surface finite element method is considered, using a regularity result of a generalized Ritz map, optimal order error estimates for the spatial discretization is shown. Combining this with the stability results for Runge–Kutta and backward differentiation formulae time integrators, we obtain convergence results for the fully discrete problems. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1200–1231, 2016