Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 52, Issue 2, Pages 601-625Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120897225
Keywords
adaptive algorithm; convergence; optimal cardinality; nonlinear; nonsymmetric
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Funding
- FWF project Adaptive Boundary Element Method - Austrian Science Fund (FWF) [P21732]
- FWF doctoral program Dissipation and Dispersion in Nonlinear PDEs [W1245]
- Austrian Science Fund (FWF) [P 21732] Funding Source: researchfish
- Austrian Science Fund (FWF) [W1245] Funding Source: Austrian Science Fund (FWF)
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We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain nonlinear second-order partial differential equations. We allow continuous polynomials of arbitrary but fixed polynomial order. The adaptivity is driven by the residual error estimator. We prove convergence even with optimal algebraic convergence rates. In particular, our analysis covers general linear second-order elliptic operators. Unlike prior works for linear nonsymmetric operators, our analysis avoids the interior node property for the refinement, and the differential operator has to satisfy a Garding inequality only. If the differential operator is uniformly elliptic, no additional assumption on the initial mesh is posed.
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