$L^2 $ Error Bounds for the Rayleigh–Ritz–Galerkin Method

Martin H. Schultz

Type: Article

Publication Date: 1971-12-01

Citations: 50

DOI: https://doi.org/10.1137/0708067

View Publication

Locations

SIAM Journal on Numerical Analysis - View

Similar Works

Action	Title	Year	Authors
+	Error bounds for the Rayleigh-Ritz-Galerkin method	1969	Martin H. Schultz
+	Rayleigh–Ritz–Galerkin Methods for Multidimensional Problems	1969	Martin H. Schultz
+	Error Estimates of Ritz—Gelerkin Methods for Indefinite Elliptic Equations	1993	Xlaohua Xuan
+ PDF Chat	Some new error estimates for Ritz–Galerkin methods with minimal regularity assumptions	1996	A. H. Schatz Junping Wang
+	Higher Order Convergence Results for the Rayleigh–Ritz Method Applied to Eigenvalue Problems. I: Estimates Relating Rayleigh–Ritz and Galerkin Approximations to Eigenfunctions	1972	J. G. Pierce R. S. Varga
+	$L^2 $-Estimates for Galerkin Methods for Second Order Hyperbolic Equations	1973	Todd Dupont
+	Some remarks on the convergence of Ritz and Galerkin methods	1973	Jan Bochenek
+	Ritz-Galerkin and other Approximate Methods	1981
+	An analysis of the Rayleigh-Ritz and refined Rayleigh-Ritz methods for nonlinear eigenvalue problems	2022	Zhongxiao Jia Qingqing Zheng
+ PDF Chat	A posteriori error estimates for nonlinear problems. Finite element discretizations of elliptic equations	1994	R. Verfürth
+	Galerkin methods and L2-error estimates for hyperbolic integro-differential equations	1989	John R. Cannon Yanping Lin Chong-Yuan Xie
+	A PRIORI L2-ERROR ESTIMATES OF THE CRANK-NICOLSON DISCONTINUOUS GALERKIN APPROXIMATIONS FOR NONLINEAR PARABOLIC EQUATIONS	2010	안민정 이민아
+	A priori L∞(L2) error estimates for finite element approximations to the wave equation with interface	2017	Bhupen Deka
+ PDF Chat	A posteriori L (L2)-error bounds for finite element approximations to the wave equation	2013	Manolis K. Georgoulis Omar Lakkis C. Makridakis
+ PDF Chat	Bounds for Eigenvalues of Some Differential Operators by the Rayleigh-Ritz Method	1965	Burton Wendroff
+ PDF Chat	Stability of the Rayleigh-Ritz-Galerkin procedure for elliptic boundary value problems	1976	Bernard J. Omodel
+	A remark on theL ? bounds of the Ritz operator associated with a finite element approximation	1986	Takashi Suzuki Hiroshi Fujita
+	Regular Methods for Solving Linear and Nonlinear Ill-Posed Problems	1984	В. А. Морозов
+	Motivation and Basic Ideas	2018	Jérôme Droniou Robert Eymard Thierry Gallouët Cindy Guichard Raphaèle Herbin
+ PDF Chat	Nonlinear eigenvalue problems and Galerkin approximations	1968	Felix E. Browder

Works That Cite This (24)

Action	Title	Year	Authors
+	Finite element methods for nonlinear elliptic systems of second order	1980	Manfred Dobrowolski Rolf Rannacher
+ PDF Chat	Quadrature-Galerkin Approximations to Solutions of Elliptic Differential Equations	1972	Martin H. Schultz
+	Two Methods of Galerkin Type Achieving Optimum $L^2 $ Rates of Convergence for First Order Hyperbolics	1974	J. E. Dendy
+ PDF Chat	Projection methods with different trial and test spaces	1976	M. S. Mock
+ PDF Chat	The effect of interpolating the coefficients in nonlinear parabolic Galerkin procedures	1975	Jim Douglas Todd Dupont
+	The finite element approximation of a coupled reaction-diffusion problem with non-Lipschitz nonlinearities	1995	John W. Barrett Patrick A. Wood
+	$L^2 $ Estimates for Galerkin Methods for Semilinear Elliptic Equations	1987	Evans M. Harrell William Layton
+ PDF Chat	Quadrature-Galerkin approximations to solutions of elliptic differential equations	1972	Martin H. Schultz
+	Stability of Galerkin multistep procedures in time-homogeneous hyperbolic problems	1980	Eckart W. Gekeler
+ PDF Chat	On the finite element approximation of solutions for radiation problem	1983	Jukka Saranen

Works Cited by This (12)

Action	Title	Year	Authors
+	Numerical methods of high-order accuracy for nonlinear boundary value Problems	1967	Philippe G. Ciarlet Martin H. Schultz R. S. Varga
+	Lectures on Elliptic Boundary Value Problems	2010	Shmuel Agmon
+ PDF Chat	Error bounds for polynomial spline interpolation	1970	Martin H. Schultz
+ PDF Chat	Elliptic spline functions and the Rayleigh-Ritz-Galerkin method	1970	Martin H. Schultz
+	Rayleigh-Ritz Approximation by Piecewise Cubic Polynomials	1966	G. Birkhoff Carl de Boor Blair Swartz Burton Wendroff
+	On higher-order numerical methods for nonlinear two-point boundary value problems	1969	Frédéric Perrin H.S. Price R. S. Varga
+	Error bounds for the Rayleigh-Ritz-Galerkin method	1969	Martin H. Schultz
+ PDF Chat	Interpolation by Ritz Approximation	1968	B.L. Hulme
+	Numerical methods of high-order accuracy for nonlinear boundary value problems	1968	Philippe G. Ciarlet Martin H. Schultz R. S. Varga
+ PDF Chat	Approximation variationnelle des problèmes aux limites	1964	Jean Céa