AnH1-Galerkin Mixed Finite Element Method for an Evolution Equation with a Positive-Type Memory Term

DOI10.1137/S0036142900372318zbMath1047.65085MaRDI QIDQ4785824

Amiya K. Pani, Graeme Fairweather

Publication date: 5 January 2003

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

convergenceevolution equationoptimal error estimatesbackward Euler methodseveral space variablesLadyshenskaya-Babuška-Brezzi consistency conditionGalerkin mixed finite element methodsemidiscrete schemesflux estimatespositive-type memory

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items

Superconvergence analysis of a two-grid method for semilinear parabolic equations ⋮ Superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{\mathrm{rot}}\) nonconforming finite element ⋮ A second-order accurate numerical method for a fractional wave equation ⋮ High accuracy analysis of an \(H^1\)-Galerkin mixed finite element method for two-dimensional time fractional diffusion equations ⋮ An \(H^1\)-Galerkin mixed finite element method for Rosenau equation ⋮ Positive definiteness of real quadratic forms resulting from the variable-step \(\mathrm{L}1\)-type approximations of convolution operators ⋮ Unconditional superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{rot}\) nonconforming finite element ⋮ A second-order BDF compact difference scheme for fractional-order Volterra equation ⋮ Numerical solution via Laplace transforms of a fractional order evolution equation ⋮ A Crank-Nicolson-type compact difference method with the uniform time step for a class of weakly singular parabolic integro-differential equations ⋮ Superconvergence analysis of anH¹-Galerkin mixed finite element method for two-dimensional multi-term time fractional diffusion equations