A Note on the Galerkin Method's Stability
Copyright policy )A Note on the Galerkin Method's Stability
AbstractNumerical stability of the Galerkin method for some class of semilinear evolution equations is studied. The stability is established in thelp(1 <p < ∞) norms. Our results are applied to the special coordinate systems. All the conditions of the stability theorems proved in this note may be readily verifiable in practice for them.
stability estimates, Numerical solutions to equations with nonlinear operators, Hilbert space, Initial value problems for linear higher-order PDEs, Nonlinear parabolic equations, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Nonlinear differential equations in abstract spaces, semilinear evolution equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Galerkin method, Higher-order parabolic equations
stability estimates, Numerical solutions to equations with nonlinear operators, Hilbert space, Initial value problems for linear higher-order PDEs, Nonlinear parabolic equations, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Nonlinear differential equations in abstract spaces, semilinear evolution equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Galerkin method, Higher-order parabolic equations
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