Finite element solution of diffusion problems with irregular data. (English) Zbl 0512.65082


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
Full Text: DOI EuDML


[1] Bartels, F.: Rotationssymmetrische Strömungen im Spalt konzentrischer Kugeln, Dissertation, TH Aachen 1978
[2] Brenner, P., Crouzeix, M., Thomée, V.: Single step methods for inhomogeneous linear differential equations in Banach space, preprint 1981
[3] Bramble, J.H., Schatz, A.H., Thomée, V., Wahlbin, L.B.: Some convergence estimates for Galerkin type approximations for parabolic equations. SIAM J. Numer. Anal.14, 218-241 (1977) · Zbl 0364.65084
[4] Ehle, B.L.: High orderA-stable methods for the numerical solution of systems of differential equations. BIT8, 276-278 (1968) · Zbl 0176.14604
[5] Grigorieff, R.D.: Numerik Gewöhnlicher Differentialgleichungen. Stuttgart: B.G. Teubner 1972 · Zbl 0249.65051
[6] Heywood, J.G., Rannacher, R.: Finite element approximation of the nonstationary Navier-Stokes problem; Part I: Regularity of solutions and second-order error estimates for spatial discretization. SIAM J. Numer. Anal.19, 275-311 (1982) Part II: Stability of solutions and error estimates uniform in time, preprint 1982; Part III: Smoothing property and higher order error estimates for spatial discretization, preprint 1982; Part IV: Convergence estimates for time discretization, in preparation · Zbl 0487.76035
[7] Lindberg, B.: On smoothing and extrapolation for the trapezoidal rule. BIT11, 29-52 (1971) · Zbl 0221.65134
[8] Luskin, M., Rannacher, R.: On the smoothing property of the Galerkin method for parabolic equations. SIAM J. Numer. Anal.19, 93-113 (1982) · Zbl 0483.65064
[9] Luskin, M., Rannacher, R.: On the smoothing property of the Crank-Nicolson scheme, Applicable Anal.14, 117-135 (1982) · Zbl 0492.65053
[10] Nassif, N.R., Descloux, J.: Stability study for time-dependent linear parabolic equations and its application to Hermitian methods. Topics in Numerical Analysis III (L. Miller (ed), pp. 239-315. New York-San Francisco-London: Academic Press 1977 · Zbl 0434.65073
[11] Rannacher, R.: Discretization of the heat equation with singular initial data. Z. Angew. Math. Mech.62, T346-T348 (1982) · Zbl 0506.76061
[12] Sammon, P.: Fully discrete approximation methods for parabolic problems with nonsmooth initial data, preprint 1981 · Zbl 0523.65069
[13] Sammon, P.: Convergence estimates for semidiscrete parabolic equation approximations. SIAM J. Numer. Anal.19, 68-92 (1982) · Zbl 0497.65056
[14] Zlamal, M.: Finite element methods for parabolic equations, Math. Comput.28, 393-404 (1974) · Zbl 0296.65054
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