scholarly journals A-priori estimates for solutions of elliptic boundary-value problems. II

1960 ◽  
Vol 63 ◽  
pp. 160-169 ◽  
Author(s):  
Felix E. Browder
Keyword(s):  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
A Priori ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Priori Estimates

scholarly journals A posteriori verification of the positivity of solutions to elliptic boundary value problems

2022 ◽  
Vol 3 (1) ◽  
Author(s):  
Kazuaki Tanaka ◽  
Taisei Asai
Keyword(s):  
Boundary Value Problems ◽  
Error Estimation ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
A Priori ◽  
Previous Method ◽  
Elliptic Boundary Value Problems ◽  
A Posteriori ◽  
Elliptic Boundary Value ◽  
Positivity Of Solutions

AbstractThe purpose of this paper is to develop a unified a posteriori method for verifying the positivity of solutions of elliptic boundary value problems by assuming neither $$H^2$$ H 2 -regularity nor $$ L^{\infty } $$ L ∞ -error estimation, but only $$ H^1_0 $$ H 0 1 -error estimation. In (J Comput Appl Math 370:112647, 2020), we proposed two approaches to verify the positivity of solutions of several semilinear elliptic boundary value problems. However, some cases require $$ L^{\infty } $$ L ∞ -error estimation and, therefore, narrow applicability. In this paper, we extend one of the approaches and combine it with a priori error bounds for Laplacian eigenvalues to obtain a unified method that has wide application. We describe how to evaluate some constants required to verify the positivity of desired solutions. We apply our method to several problems, including those to which the previous method is not applicable.

Numerical solution of elliptic boundary-value problems for Schrödinger-type equations using the Kantorovich method

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
A.A. Gusev ◽  
O. Chuluunbaatar ◽  
S.I. Vinitsky ◽  
A.G. Abrashkevich ◽  
V.L. Derbov
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problems ◽  
Kantorovich Method ◽  
Elliptic Boundary Value

scholarly journals Parallel black box $$\mathcal {H}$$ -LU preconditioning for elliptic boundary value problems

2008 ◽  
Vol 11 (4-6) ◽  
pp. 273-291 ◽  
Author(s):  
Lars Grasedyck ◽  
Ronald Kriemann ◽  
Sabine Le Borne
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Black Box ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value

Improved scales of spaces and elliptic boundary-value problems. I

2006 ◽  
Vol 58 (2) ◽  
pp. 244-262 ◽  
Author(s):  
V. A. Mikhailets ◽  
A. A. Murach
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value
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