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000914972 020__ $$a9783030237882$$q(electronic book)
000914972 020__ $$a3030237885$$q(electronic book)
000914972 020__ $$z9783030237875
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000914972 035__ $$aSP(OCoLC)on1121487032
000914972 035__ $$aSP(OCoLC)1121487032
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000914972 1001_ $$aLangtangen, Hans Petter,$$d1962-
000914972 24510 $$aIntroduction to numerical methods for variational problems /$$cHans Petter Langtangen, Kent-Andre Mardal.
000914972 260__ $$aCham :$$bSpringer,$$c2019.
000914972 300__ $$a1 online resource
000914972 336__ $$atext$$btxt$$2rdacontent
000914972 337__ $$acomputer$$bc$$2rdamedia
000914972 338__ $$aonline resource$$bcr$$2rdacarrier
000914972 4901_ $$aTexts in computational science and engineering ;$$v21
000914972 5050_ $$aIntro; Preface; Second Preface; Contents; List of Exercises and Problems; 1 Quick Overview of the Finite Element Method; 2 Function Approximation by Global Functions; 2.1 Approximation of Vectors; 2.1.1 Approximation of Planar Vectors; 2.1.2 Approximation of General Vectors; 2.2 Approximation Principles; 2.2.1 The Least Squares Method; 2.2.2 The Projection (or Galerkin) Method; 2.2.3 Example of Linear Approximation; 2.2.4 Implementation of the Least Squares Method; 2.2.5 Perfect Approximation; 2.2.6 The Regression Method; 2.3 Orthogonal Basis Functions; 2.3.1 Ill-Conditioning
000914972 5058_ $$a2.3.2 Fourier Series2.3.3 Orthogonal Basis Functions; 2.3.4 Numerical Computations; 2.4 Interpolation; 2.4.1 The Interpolation (or Collocation) Principle; 2.4.2 Lagrange Polynomials; 2.4.3 Bernstein Polynomials; 2.5 Approximation Properties and Convergence Rates; 2.6 Approximation of Functions in Higher Dimensions; 2.6.1 2D Basis Functions as Tensor Products of 1D Functions; 2.6.2 Example on Polynomial Basis in 2D; 2.6.3 Implementation; 2.6.4 Extension to 3D; 2.7 Exercises; Problem 2.1: Linear Algebra Refresher; Problem 2.2: Approximate a Three-Dimensional Vector in a Plane
000914972 5058_ $$aProblem 2.3: Approximate a Parabola by a SineProblem 2.4: Approximate the Exponential Function by Power Functions; Problem 2.5: Approximate the Sine Function by Power Functions; Problem 2.6: Approximate a Steep Function by Sines; Problem 2.7: Approximate a Steep Function by Sines with Boundary Adjustment; Exercise 2.8: Fourier Series as a Least Squares Approximation; Problem 2.9: Approximate a Steep Function by Lagrange Polynomials; Problem 2.10: Approximate a Steep Function by Lagrange Polynomials and Regression; 3 Function Approximation by Finite Elements; 3.1 Finite Element Basis Functions
000914972 5058_ $$a3.1.1 Elements and Nodes3.1.2 The Basis Functions; 3.1.3 Example on Quadratic Finite Element Functions; 3.1.4 Example on Linear Finite Element Functions; 3.1.5 Example on Cubic Finite Element Functions; 3.1.6 Calculating the Linear System; 3.1.7 Assembly of Elementwise Computations; 3.1.8 Mapping to a Reference Element; 3.1.9 Example on Integration over a Reference Element; 3.2 Implementation; 3.2.1 Integration; 3.2.2 Linear System Assembly and Solution; 3.2.3 Example on Computing Symbolic Approximations; 3.2.4 Using Interpolation Instead of Least Squares
000914972 5058_ $$a3.2.5 Example on Computing Numerical Approximations3.2.6 The Structure of the Coefficient Matrix; 3.2.7 Applications; 3.2.8 Sparse Matrix Storage and Solution; 3.3 Comparison of Finite Elements and Finite Differences; 3.3.1 Finite Difference Approximation of Given Functions; 3.3.2 Interpretation of a Finite Element Approximation in Terms of Finite Difference Operators; 3.3.3 Making Finite Elements Behave as Finite Differences; 3.4 A Generalized Element Concept; 3.4.1 Cells, Vertices, and Degrees of Freedom; 3.4.2 Extended Finite Element Concept; 3.4.3 Implementation
000914972 506__ $$aAccess limited to authorized users.
000914972 650_0 $$aVariational inequalities (Mathematics)
000914972 650_0 $$aFinite element method.
000914972 7001_ $$aMardal, Kent-Andre.
000914972 77608 $$iPrint version: $$z3030237877$$z9783030237875$$w(OCoLC)1102474432
000914972 830_0 $$aTexts in computational science and engineering ;$$v21.
000914972 852__ $$bebk
000914972 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-23788-2$$zOnline Access$$91397441.1
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