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Finite‐volume schemes for Friedrichs systems in multiple space dimensions: A priori and a posteriori error estimates
Author(s) -
Jovanović Vladimir,
Rohde Christian
Publication year - 2005
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.20026
Subject(s) - a priori and a posteriori , mathematics , finite volume method , polygon mesh , space (punctuation) , partial differential equation , class (philosophy) , finite element method , mathematical analysis , geometry , computer science , operating system , thermodynamics , philosophy , physics , epistemology , artificial intelligence , mechanics
We consider a class of finite‐volume schemes on unstructured meshes for symmetric hyperbolic linear systems of balance laws in two and three space dimensions. This class of schemes has been introduced and analyzed by Vila and Villedieu (1998). They have proven an a priori error estimate for approximations of smooth solutions. We extend the results to weak solutions. This is the base to derive an a posteriori error estimate for finite‐volume approximations of weak solutions. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005