Analyticity, maximal regularity and maximum-norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra
Copyright policy )Analyticity, maximal regularity and maximum-norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra
In general polygons and polyhedra, possibly nonconvex, the analyticity of the finite element heat semigroup in the $L^q$ norm, $1\leq q\leq\infty$, and the maximal $L^p$-regularity of semi-discrete finite element solutions of parabolic equations are proved. By using these results, the problem of maximum-norm stability of the finite element parabolic projection is reduced to the maximum-norm stability of the Ritz projection, which currently is known to hold for general polygonal domains and convex polyhedral domains.
- Hong Kong Polytechnic University China (People's Republic of)
- Hong Kong Polytechnic University (香港理工大學) China (People's Republic of)
- Hong Kong Polytechnic University (香港理工大學) Hong Kong
Nonconvex polyhedra, Parabolic equation, Finite element method, parabolic equation, Smoothness and regularity of solutions to PDEs, Heat equation, finite element method, analytic semigroup, Numerical Analysis (math.NA), maximal \(L^p\)-regularity, 510, Maximum principles in context of PDEs, nonconvex polyhedra, Initial-boundary value problems for second-order parabolic equations, Analytic semigroup, Maximum-norm stability, FOS: Mathematics, Maximal Lp-regularity, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Stability in context of PDEs, maximum-norm stability
Nonconvex polyhedra, Parabolic equation, Finite element method, parabolic equation, Smoothness and regularity of solutions to PDEs, Heat equation, finite element method, analytic semigroup, Numerical Analysis (math.NA), maximal \(L^p\)-regularity, 510, Maximum principles in context of PDEs, nonconvex polyhedra, Initial-boundary value problems for second-order parabolic equations, Analytic semigroup, Maximum-norm stability, FOS: Mathematics, Maximal Lp-regularity, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Stability in context of PDEs, maximum-norm stability
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