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      KCI등재 SCIE SCOPUS

      A PRIORI L² ERROR ANALYSIS FOR AN EXPANDED MIXED FINITE ELEMENT METHOD FOR QUASILINEAR PSEUDO-PARABOLIC EQUATIONS

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      https://www.riss.kr/link?id=A103363752

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      다국어 초록 (Multilingual Abstract)

      Based on an expanded mixed finite element method, we con- sider the semidiscrete approximations of the solution u of the quasilinear pseudo-parabolic equation defined on Ω ⊂ R d , 1 ≤ d ≤ 3. We construct the semidiscrete approximations of ∇u and a(u)∇u + b(u)∇u t as well as u and prove the existence of the semidiscrete approximations. And also we prove the optimal convergence of ∇u and a(u)∇u + b(u)∇u t as well as u in L² normed space.
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      Based on an expanded mixed finite element method, we con- sider the semidiscrete approximations of the solution u of the quasilinear pseudo-parabolic equation defined on Ω ⊂ R d , 1 ≤ d ≤ 3. We construct the semidiscrete approximations of ∇u...

      Based on an expanded mixed finite element method, we con- sider the semidiscrete approximations of the solution u of the quasilinear pseudo-parabolic equation defined on Ω ⊂ R d , 1 ≤ d ≤ 3. We construct the semidiscrete approximations of ∇u and a(u)∇u + b(u)∇u t as well as u and prove the existence of the semidiscrete approximations. And also we prove the optimal convergence of ∇u and a(u)∇u + b(u)∇u t as well as u in L² normed space.

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      참고문헌 (Reference)

      1 F. Brezzi, "Two families of mixed finite elements for second order elliptic problems" 47 (47): 217-235, 1985

      2 R. E. Ewing, "Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations" 15 (15): 1125-1150, 1978

      3 D. N. Arnold, "Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable" 36 (36): 53-63, 1981

      4 R. W. Carroll, "Singular and Degenerate Cauchy Problems" Academic Press 1976

      5 P. J. Chen, "On a theory of heat conduction involving two temperatures" 19 (19): 614-627, 1968

      6 D. Shi, "Nonconforming H1-Galerkin mixed FEM for Sobolev equations on anisotropic meshes" 25 (25): 335-344, 2009

      7 Y. Chen, "Lp error estimates of two-grid schemes of expanded mixed finite element methods" 209 (209): 197-205, 2009

      8 F. Gao, "Local discontinuous Galerkin finite element method and error estimates for one class of Sobolev equation" 41 (41): 436-460, 2009

      9 D. Shi, "High accuracy analysis of a new nonconforming mixed finite element scheme for sobolev equation" 218 (218): 3176-3186, 2011

      10 J. Jr. Douglas, "Global estimates for mixed methods for second order elliptic equations" 44 (44): 39-52, 1985

      1 F. Brezzi, "Two families of mixed finite elements for second order elliptic problems" 47 (47): 217-235, 1985

      2 R. E. Ewing, "Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations" 15 (15): 1125-1150, 1978

      3 D. N. Arnold, "Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable" 36 (36): 53-63, 1981

      4 R. W. Carroll, "Singular and Degenerate Cauchy Problems" Academic Press 1976

      5 P. J. Chen, "On a theory of heat conduction involving two temperatures" 19 (19): 614-627, 1968

      6 D. Shi, "Nonconforming H1-Galerkin mixed FEM for Sobolev equations on anisotropic meshes" 25 (25): 335-344, 2009

      7 Y. Chen, "Lp error estimates of two-grid schemes of expanded mixed finite element methods" 209 (209): 197-205, 2009

      8 F. Gao, "Local discontinuous Galerkin finite element method and error estimates for one class of Sobolev equation" 41 (41): 436-460, 2009

      9 D. Shi, "High accuracy analysis of a new nonconforming mixed finite element scheme for sobolev equation" 218 (218): 3176-3186, 2011

      10 J. Jr. Douglas, "Global estimates for mixed methods for second order elliptic equations" 44 (44): 39-52, 1985

      11 Y. Lin, "Galerkin methods for nonlinear Sobolev equations" 40 (40): 54-66, 1990

      12 Y. Lin, "Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions" 165 (165): 180-191, 1992

      13 M. T. Nakao, "Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension" 47 (47): 139-157, 1985

      14 T. Sun, "Error estimates for a discontinuous Galerkin method with interior penalties applied to nonlinear Sobolev equations" 24 (24): 879-896, 2008

      15 Y. Cao, "Cauchy problems of semilinear pseudo-parabolic equations" 246 (246): 4568-4590, 2009

      16 G. I. Barenblatt, "Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks" 24 : 1286-1303, 1960

      17 D. N. Arnold, "An interior penalty finite element method with discontinuous elements" 19 (19): 724-760, 1982

      18 F. Gao, "A split least-squares characteristic mixed finite element method for sobolev equations with convection term" 80 (80): 341-351, 2009

      19 H. Guo, "A remark on split least-squares mixed element procedures for pseudo-parabolic equations" 217 (217): 4682-4690, 2011

      20 P. L. Davis, "A quasilinear parabolic and related third order problem" 49 : 327-335, 1972

      21 T. Sun, "A priori error estimates for interior penalty discontinuous Galerkin method applied to nonlinear Sobolev equations" 200 (200): 147-159, 2008

      22 D. Kim, "A posteriori error estimator for expanded mixed hybrid methods" 23 (23): 330-349, 2007

      23 P. A. Raviart, "A mixed finite element method for 2nd order elliptic problems, Mathematical aspects of finite element methods" 292-315, 1977

      24 T. W. Ting, "A cooling process according to two-temperature theory of heat conduction" 45 : 23-31, 1974

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